Preheat oven to 400°F (200°C). Pat chicken drumsticks dry and season with salt, pepper, and smoked paprika.
Heat olive oil over medium-high heat in an ovenproof skillet. Sear chicken drumsticks until golden on all sides, about 5–6 minutes.
Transfer skillet to oven and roast chicken for 20–25 minutes until fully cooked.
While chicken roasts, melt butter in a saucepan over medium heat. Sauté onion and garlic until translucent.
Add thyme, red pepper flakes, and flour to the saucepan, cooking for 1 minute to remove raw flour taste.
Slowly whisk in chicken broth and simmer until sauce thickens slightly.
Stir in heavy cream, tomato paste, and Dijon mustard. Simmer gently for 5–6 minutes, then add chopped parsley.
Return chicken to stovetop, pour sauce over drumsticks, and simmer for 2–3 minutes.
Serve chicken and sauce hot over cooked white rice, garnished with additional parsley.