Preheat the oven to 425 degrees F.: The warm, dry heat readying the oven is essential because a properly preheated oven ensures the biscuits rise quickly and brown on the outside while staying tender within. You should feel a burst of hot air when you open the oven and hear a faint hum as it cycles. If you skip preheating, biscuits can spread and become dense rather than fluffy. Common mistake to avoid, do not set the oven too low or the biscuits will take too long to set and may become soggy from the filling's steam.
In a deep 12-inch cast iron skillet or oven safe Dutch oven, melt the butter over medium high heat. Add the onion, carrots, and celery; cook until tender, stirring occasionally, about 5 minutes. Add the garlic and cook for 1 minute.: You will notice the butter foam and then settle as it melts, releasing a warm, nutty aroma. The vegetables will soften and the onion becomes translucent, offering a sweet scent that signals they are ready. The garlic added at the end will release a sharp, fragrant note without turning bitter because it cooks briefly. This step develops the aromatic base, helping the final filling taste layered. A frequent misstep is browning the garlic too early, which yields bitterness, so add it after the vegetables have softened.
Stir in flour until lightly browned, about 1 minute. Add the thyme, salt, and pepper.: As you stir, the flour will coat the vegetables and start to toast, creating a slightly nutty smell and helping to eliminate any raw flour taste. This toasting also builds a roux like base that thickens the sauce when liquid is added. The dried thyme and seasoning added now become toasty and integrated, not sharp. If you skip the brief cook, you might end up with a grainy sauce, so make sure the flour loses its raw white sheen.
Slowly pour in the chicken broth and heavy cream. Bring to a boil; reduce heat and simmer, stirring occasionally, until slightly thickened, about 3 to 5 minutes.: Pouring gradually lets the liquid incorporate smoothly so the mixture becomes glossy and uniform rather than lumpy, and you will hear a soft simmer that deepens into a gentle bubble as proteins and starches bind. The aroma turns richer and creamier, and the sauce will cling to the spoon when it is properly thickened. Avoid high rolling boils which can separate the cream or scorch the bottom; use steady heat and stir to prevent sticking.
Stir in the chicken, peas, and parsley. Season with additional salt and pepper, if necessary. Turn off the heat and set aside while you make the biscuits.: When you fold in the shredded chicken , the filling takes on substance and the meat warms through, releasing savory notes. The frozen peas add bright color and small bursts of sweetness, while the fresh parsley lifts the whole mixture. Taste and correct seasoning now because the biscuit topping will mute some saltiness. A common issue is overseasoning early, so taste after adding the final ingredients and adjust cautiously.
To make the biscuits, whisk together the flour, baking powder, baking soda, sugar, and salt in a large bowl. Set aside.: Dry ingredients combine into a fine, pale mix and you may notice a faint, bready smell. Even distribution of leaveners matters to ensure uniform lift, so whisk thoroughly. If you under-mix, some biscuits may not rise properly and will be dense; if you overwork later, the biscuits may become tough, so keep this step efficient.
In a medium bowl, combine cold buttermilk and the 1/2 cup slightly cooled melted butter. Stir with a spatula until combined and small clumps form. It is ok if the mixture is lumpy.: The cold buttermilk keeps reactions under control, and the melted butter enriches the dough. Stirring yields small, chunky curdled bits that create flaky pockets when baked, and you will notice the mixture is thicker than plain milk. If the butter is too hot it can activate leaveners prematurely or melt the butter in the dough unevenly, so let it cool slightly before combining.
Add buttermilk mixture to dry ingredients and stir with rubber spatula until just combined and the biscuit batter pulls away from sides of bowl.: The batter will look shaggy and slightly sticky, with visible lumps that indicate tender biscuits to come. Stop mixing once it holds together to avoid gluten development which makes biscuits tough. If you overmix, the texture becomes chewy instead of tender, so resist the urge to keep stirring.
Use a large cookie scoop or a greased 1/4 cup measuring cup to scoop out the dough. Drop the biscuit dough on top of the filling, leaving a little space between each biscuit because they will spread a little in the oven. Brush with the extra melted butter.: Dropping the dough creates mounds that will rise and form a golden crust; the brushed butter adds shine and rich aroma as it melts into crevices. You will hear a soft hiss as the cold dough meets the hot filling if it is warm enough, and the biscuits will settle slightly before rising. Placing them too close can cause them to merge into an uneven crust, so space them with intention.
Carefully transfer the skillet to the hot oven and bake for 14 to 17 minutes or until the biscuits are lightly golden brown on top.: The oven will transform the dough into a browned top that yields a faint toasty scent and a flaky interior, while the filling bubbles gently at the edges. Look for an even golden color on the biscuits and a gently bubbling filling as cues that everything is cooked through. Opening the oven too often lengthens bake time and can cause uneven rise, so check near the end of the time window.
Remove from oven and let stand for 10 minutes before serving.: Allowing the skillet to rest helps the filling settle and thicken slightly, making serving cleaner and the textures more harmonious. The steam will calm and flavors meld during this short wait, and you will still have warm, comforting bites after resting. Cutting into it too soon can cause the filling to run and make serving messy, so be patient for the best presentation.