Heat the butter and olive oil in a large Dutch oven over medium-high heat.
Season the chicken with the salt, pepper, smoked paprika, and garlic powder.
Add the chicken in a single layer and cook for 6–7 minutes, turning occasionally, until lightly browned. Transfer to a plate.
In the same pot, add the onion, celery, and carrots. Cook for about 5 minutes until softened.
Stir in the garlic and cook for 30 seconds until fragrant.
Sprinkle the flour over the vegetables and stir continuously for 1 minute.
Slowly whisk in the chicken broth, scraping the bottom of the pot to release any browned bits.
Add the diced potatoes, thyme, and dried parsley. Bring to a gentle boil.
Reduce the heat, cover, and simmer for 15–18 minutes until the potatoes are fork tender.
Return the cooked chicken to the pot.
Stir in the corn and simmer for 5 minutes.
Reduce the heat to low and slowly stir in the heavy cream and milk.
Heat gently for 3–5 minutes without boiling.
Taste and adjust the seasoning if needed.
Stir in the fresh parsley and serve warm with your favorite toppings.