Prepare the chicken: Pat chicken thighs dry with paper towels and season generously with salt and pepper on both sides. This ensures proper browning and flavor development.
Sear the chicken: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Once hot, place chicken skin-side down and sear until golden brown, about 5-6 minutes. Flip and cook the other side for 3-4 minutes. Remove chicken to a plate and set aside.
Sauté the aromatics: In the same pan with the chicken drippings, add the remaining tablespoon of butter. Add onions and cook until translucent, about 3-4 minutes. Add mushrooms and cook until they release their moisture and begin to brown, about 5 minutes.
Build the flavor base: Add minced garlic and cook for 30 seconds until fragrant. Sprinkle flour over the vegetables and stir constantly for 1-2 minutes to cook out the raw flour taste.
Create the sauce: Slowly pour in chicken broth while stirring continuously to prevent lumps. Bring to a simmer and let it thicken slightly, about 3-4 minutes. Stir in heavy cream, thyme, paprika, and rosemary.
Return chicken to pan: Nestle the chicken thighs back into the sauce, skin-side up. Reduce heat to low, cover, and simmer for 15-20 minutes until chicken is completely cooked through (internal temperature of 165°F).
Finish and serve: Taste sauce and adjust seasoning with salt and pepper as needed. Serve chicken and sauce over warm rice, garnished with fresh parsley if desired.