Bake potato (whole, unpeeled) in microwave for 8-10 minutes or until soft in the center. Allow it to cool slightly and peel the potato. Mash the peeled potato with the cream cheese as if you were making mashed potatoes; set aside.: The scent of warm potato is comforting, and the skin will feel tender when pierced with a fork. After microwaving, let it sit a few minutes so the steam finishes the cook and it is safe to handle. When you peel, the flesh should flake easily; if it resists, return it to the microwave in short bursts. A common mistake is peeling while too hot, which can scald your fingers, so use a towel or let it cool slightly.
Add olive oil to a large pot. Add the onion and cook it for 5-6 minutes, or until softened.: You will notice a gentle earthy aroma as you remove the skin, and the interior should be fluffy rather than gummy. Cooling a touch helps the potato keep structure as you mash it. If the interior seems watery, it may have been undercooked; microwave briefly until fully tender.
Add the garlic and flour to onion, stirring for about a minute. Slowly pour in the chicken broth and evaporated milk, stirring continuously to break up any chunks.: The texture should become luxuriously smooth and slightly glossy as the cream cheese melts into the warm potato . Use a fork or small masher and press until lumps disappear. If the mash is cool and the cream cheese resists blending, warm gently to prevent grudgy bits. Overworking starchy potatoes can make them gluey, so mash just until combined.
Next stir in the mashed potato mixture, salt, pepper, and broccoli. Bring this to a low simmer for 8-10 minutes until it has thickened. Blend with the immersion blender for about a minute until the mixture is creamy.: When the olive oil shimmers faintly, it is ready to accept the aromatics. Pouring the oil into a cold pot prevents splatter and allows for even heating. If the oil smokes, reduce heat immediately to avoid imparting bitterness to the entire dish.
Turn the heat off and stir in the cheese until it has melted.: As the onion sweats, you will notice it turning translucent and releasing sweet, savory notes. Stir occasionally so the pieces cook evenly and do not brown too quickly. If the onion starts to brown, lower the heat because caramelization will change the flavor profile more than we want here.
Add the garlic and flour to onion, stirring for about a minute: The brief toasting will eliminate raw flour taste and awaken the garlic aroma. You should detect a nutty scent from the flour and a bright, savory hit from the garlic . Stir constantly to avoid burning, because burnt garlic will make the base bitter.
Slowly pour in the chicken broth and evaporated milk, stirring continuously to break up any chunks: As the liquid hits the pot, you will hear a soft simmer begin and see the mixture loosen. Continuous stirring prevents lumps and creates a glossy, cohesive base. Stop and scrape the pot bottom if any dry flour gathers, and taste the broth because canned stocks vary in salt; adjust later to avoid over seasoning.
Next stir in the mashed potato mixture, salt, pepper, and broccoli: When the mash joins the pot, the texture will thicken noticeably and look velvety. The frozen broccoli will cool the liquid briefly, so expect a quiet sizzle as it returns to a simmer. Season gradually with salt and black pepper , because you can always add more at the end. A common error is dumping all seasonings at once, which can’t be undone.
Bring this to a low simmer for 8 to 10 minutes until it has thickened: Gentle bubbling around the pot edge signals the right simmer, and the aroma will deepen into an inviting, stew like scent. The soup should coat the back of a spoon when ready; if it seems too thin, simmer a bit longer. Avoid a rolling boil, which can break emulsions and change the texture.
Blend with the immersion blender for about a minute until the mixture is creamy: Swirl the blender slowly and you will see the soup transform into a smooth, uniform color and texture. The action releases steam, so keep the blade submerged to prevent splatter. If you prefer chunks of broccoli , pulse briefly rather than fully pureeing. Over blending can remove desirable texture, so stop when it looks luscious and cohesive.
Turn the heat off and stir in the cheese until it has melted: With the pot off the stove, the residual warmth melts the cheddar cheese into a glossy finish without risking separation. Stir gently until the cheese is fully integrated and the surface looks silky. If the cheese clumps, a splash of warm broth can smooth it out. Avoid overheating after adding cheese, because excessive heat can make it grainy.