Pat chicken drumsticks dry and season all over with paprika, salt, black pepper, and garlic powder.
Heat olive oil in a large deep skillet over medium-high heat.
Sear drumsticks 3-4 minutes per side until golden; remove and set aside.
Melt butter in the same skillet over medium heat.
Add minced garlic and chopped onion; cook until soft and fragrant.
Stir in chopped cilantro and pour in chicken broth, scraping up browned bits.
Return chicken to the skillet, spoon sauce over the top, cover, and simmer 15-18 minutes until cooked through.
Uncover, raise heat slightly, and simmer 2-3 minutes more to thicken the sauce.
Serve hot with extra sauce spooned over the drumsticks.