Pat the chicken pieces dry with paper towels. Season generously with salt and pepper.

Place the flour in a shallow dish. Dredge each piece of chicken in the flour, making sure to coat it evenly. Shake off any excess flour.

Heat the olive oil in a large skillet over medium-high heat. Add the chicken to the skillet in a single layer, being careful not to overcrowd the pan. You may need to work in batches. Brown the chicken on all sides until golden brown, about 5-7 minutes per side. Remove the chicken from the skillet and set aside.

Add the chopped onion to the skillet and cook until softened, about 5 minutes. Add the minced garlic and cook for another minute, until fragrant.

Sprinkle the remaining flour over the onions and garlic. Cook for 1-2 minutes, stirring constantly, to create a roux.

Gradually whisk in the chicken broth, making sure to scrape up any browned bits from the bottom of the skillet.

Add the fresh thyme (if using), bay leaf (if using), and smoked paprika (if using) to the gravy. Season with salt and pepper to taste.

Return the chicken to the skillet, nestling it into the gravy. Bring the gravy to a simmer, then reduce the heat to low, cover the skillet, and simmer for 30-45 minutes, or until the chicken is cooked through and tender. The internal temperature should reach 165°F (74°C).

Remove the skillet from the heat. Stir in the heavy cream. Taste and adjust the seasonings as needed. For extra richness, stir in a tablespoon of butter.

Serve the smothered chicken hot, spooning the gravy over mashed potatoes, rice, or your favorite side dish. Garnish with fresh parsley, if desired.