Cut chicken breasts in half widthwise to create 4 thinner pieces. Pound each piece to even out thickness. Season both sides with Italian seasoning, garlic powder, salt, and pepper.: The moment you pound and season the chicken you set the stage for even cooking and consistent flavor. As you gently pound, listen for a soft, almost muffled thud rather than a loud smack, and feel the meat relax under the mallet, which helps it cook through quickly and evenly. Seasoning both sides early lets the spices adhere and begin to infuse, so you will smell the herby, garlicky aroma even before the pan heats. A common mistake is pounding too thin, which can make the chicken dry when cooked; aim for uniform thickness rather than paper thin.
In a large pot, heat 2 tablespoons olive oil over medium-high heat. Cook chicken until it’s 160°F all the way through and the juices run clear, about 3–4 minutes. Transfer chicken to a plate, cover with foil, and let it rest for 5 minutes. Slice, dice, or shred the chicken.: As the chicken sizzles in the oil you will hear a steady, confident sound and smell those browned, caramelized notes. When the exterior is golden and the thermometer reads 160°F, the meat will still be moist after resting, since carryover heat finishes cooking. Resting under foil keeps juices locked in, and slicing or shredding afterward gives you tender pieces that integrate into the soup. Avoid overcrowding the pot which can cause steaming instead of browning, leaving you without that flavorful fond.
Without wiping it out, add 1 tablespoon oil and 1 tablespoon butter to the same pot you cooked the chicken in. Add mirepoix; sauté for 5–7 minutes. Add minced garlic, chicken bouillon powder, and diced potatoes; sauté for 1 minute.: Using the same pot lets you harness the browned bits left behind, and adding butter with oil offers both flavor and a higher smoke point. The mirepoix will soften and release a sweet, savory aroma, and you should see the edges of the vegetables go translucent with occasional gentle browning. Adding garlic late prevents it from burning and turning bitter, while the potatoes get a quick toss to pick up those flavors. Watch closely and stir often so the garlic does not scorch, which would create a harsh taste.
Pour in chicken broth and bring to a boil. Reduce heat, cover pot, and simmer for 10–15 minutes until potatoes are fork tender.: When the broth hits a boil, it will steam and shimmer, and that rolling motion means flavors are amalgamating. Lowering to a simmer and covering concentrates heat for even cooking, and testing the potatoes with a fork is the best indicator they are done, feeling tender but not falling apart. Simmering too long can make the potatoes mushy, so check early; undercooked potatoes will remain firm in the center, so patience here ensures good texture.
In a separate medium pot, melt 4 tablespoons butter over medium heat. Whisk in flour and cook for 1 minute. Gradually add milk while whisking continuously until smooth. Cook until the mixture thickens, then stir in heavy cream. Keep warm, whisking occasionally.: This roux plus milk technique creates a silky, lump free base that gives the soup body. As you whisk, you should see the mixture go from glossy to slightly thickened, with a gentle simmer and faint bubbling at the edges. Adding milk slowly while whisking prevents clumps, and stirring in the heavy cream enriches the texture. A common pitfall is adding cold milk too quickly, which can cause lumps; keep the milk slightly warm or add it gradually to preserve a smooth sauce.
Pour the milk and cream mixture into the soup. Reduce heat to low. Gradually add shredded cheese, a handful at a time, stirring between additions until melted. Return cooked chicken to the pot. If desired, add frozen peas and stir until warmed. Taste and adjust seasonings as needed.: As the dairy blends with the broth you will notice the soup thicken and the aroma become creamier. Adding Cheddar cheese slowly helps it melt into the mixture rather than clumping; each handful should disappear into a silky ribbon, and the soup will grow richer and slightly glossy. Reintroducing the shredded chicken lets its juices mingle with the creamy base, while the frozen peas will pop with color and a mild sweetness when warmed. Taste at this stage because cheese and bouillon can increase saltiness, so adjust gradually; overheating can cause dairy to separate, so keep the heat low.
Enjoy the soup warm, garnished with freshly chopped parsley or thyme. Serve with hearty buttered bread if desired.: The final bowl should steam gently and carry a layered aroma of herbs, chicken , and melted Cheddar cheese . A sprinkle of fresh herbs brightens each spoonful, and dunking hearty buttered bread into the bowl amplifies comfort. If the soup seems too thick once cooled, a splash of warm broth loosens it without diluting flavor. Avoid boiling after adding cheese and cream, which can alter the texture and make it grainy.