Preheat the oven to 325°F with a rack set in the lower-middle position.
Pat the chicken thighs dry with paper towels. Season both sides with salt and pepper.
Heat the olive oil in a 12-inch oven-safe stainless steel skillet over medium-high heat. Add the chicken skin-side down and cook 7 minutes without moving it, until the skin is well browned. Flip and cook 3 minutes on the other side. Transfer the chicken to a plate.
Carefully pour off all but about 2 tablespoons of fat from the skillet. Add the shallot and garlic and cook for about 1½ minutes, until softened but not browned.
Add the wine, red wine vinegar, and chicken broth. Bring to a simmer, scraping up the browned bits from the bottom of the skillet.
Return the chicken to the skillet, skin-side up. The chicken should not be fully submerged. Transfer the skillet to the oven and bake uncovered for 40–45 minutes, until the internal temperature reaches about 195°F.
Remove the chicken to a serving dish. Return it to the turned-off oven, loosely covered, to keep warm while you finish the sauce.
Place the skillet back on the stovetop over high heat. Stir in the tomato paste, rosemary, and thyme. Reduce the sauce to about 1¼ cups, about 10 minutes. Turn off the heat and stir in the butter until smooth.
Taste and adjust seasoning with salt and pepper. Spoon the sauce over the chicken and serve.