Season chicken generously on both sides with salt. Heat olive oil in a heavy, deep-sided pan with a lid over high heat. Add chicken, skin-side down, and cook until well browned, about 5 minutes. Flip and cook until browned on the other side, 3 to 4 minutes. Turn off heat. Transfer chicken to a plate and set aside. Spoon out excess chicken fat, if desired.

Add onions and a pinch of salt to the same pan and sauté over medium until golden, about 5 minutes. Add garlic, tomato paste, and flour and cook, stirring, another 3 to 4 minutes to form a tomato roux. Stir in 1 teaspoon kosher salt, freshly ground black pepper, smoked paprika, sweet paprika, and cayenne; cook for 1 minute. Add chicken broth and bring to a simmer over high heat.

Reduce heat to medium-low and transfer chicken and accumulated juices back into the pan. Baste the tops with the sauce, cover the pan with the lid, and simmer, basting occasionally with the sauce, until the chicken is no longer pink in the centers and is fork-tender, 45 to 60 minutes. Remove the chicken and transfer to a plate.

Skim some fat off the top of the sauce if desired. Whisk heavy cream and sour cream into the sauce and bring to a simmer, stirring occasionally. Transfer the chicken and any juices back into the sauce. Simmer, uncovered, basting often, until chicken is heated through and very tender, about 10 minutes. Taste and adjust seasoning if needed.