In a shallow bowl, combine flour, salt, pepper, and paprika.
Pat chicken dry and dredge each piece in the flour mixture, shaking off excess. Reserve 1 tablespoon of the seasoned flour.
Heat vegetable oil in a large heavy skillet over medium-high heat.
Place chicken skin-side down in the skillet and sear until golden brown, approximately 5-6 minutes per side. Remove chicken and set aside.
Lower heat to medium and add butter and sliced onions to the skillet. Cook until onions are soft and caramelized, about 8-10 minutes.
Add garlic and the reserved tablespoon of flour to the onions; cook for 1 minute while stirring constantly.
Slowly pour in chicken broth and add thyme, whisking to incorporate the flour and scraping the bottom of the pan to release browned bits.
Return chicken thighs to the skillet, skin-side up. Reduce heat to low, cover, and simmer for 25-30 minutes until chicken reaches an internal temperature of 165 degrees Fahrenheit.
Serve chicken topped with the onion gravy, ideally over mashed potatoes or white rice.