Sauté the aromatics: In a large pot or Dutch oven, warm the butter and oil over medium heat.
Add onion, carrots, and celery. Cook, stirring occasionally, until softened, about 6–8 minutes. Add garlic and cook 30 seconds, just until fragrant.
Season and build flavor: Stir in salt, pepper, thyme, and poultry seasoning.
Let the spices bloom for 30–60 seconds so they become aromatic.
Make the roux: Sprinkle the flour over the vegetables and stir to coat. Cook for 1–2 minutes to remove the raw flour taste. It will look a bit pasty—this is good.
Add the liquids: Slowly pour in the chicken broth while whisking or stirring constantly to avoid lumps.
Add the diced potato if using. Bring to a gentle simmer.
Simmer to thicken: Cook 10–12 minutes, stirring occasionally, until the potatoes are tender and the soup has thickened slightly.
Stir in the creaminess: Lower the heat and pour in the milk or half-and-half. Do not boil after adding dairy; keep it at a gentle simmer.
Add the chicken and veggies: Stir in the cooked chicken, peas, and corn.
Simmer 3–5 minutes, just to warm through and marry the flavors.
Finish and balance: Stir in parsley and lemon juice. Taste and adjust with more salt and pepper as needed. If it’s too thick, splash in a bit more broth or milk until it’s just right.
Serve: Ladle into bowls and top with cracked pepper.
Add biscuit crackers or a warm roll on the side for that “pot pie” vibe.