Pat the chicken thighs completely dry with paper towels. Season liberally on all sides with kosher salt and black pepper.
Heat olive oil in a large Dutch oven or heavy-bottomed skillet over medium-high heat. Once shimmering, place chicken thighs skin-side down.
Sear undisturbed for 6-8 minutes until the skin is deep golden brown and crispy. Flip and cook for 2 more minutes. Remove chicken to a plate and set aside.
Drain all but 1 tablespoon of rendered fat from the pan. Reduce heat to medium.
Add the smashed garlic cloves and rosemary sprigs. Sauté for 1-2 minutes until fragrant and garlic is lightly browned.
Pour in the white wine to deglaze the pan, using a wooden spoon to scrape up the browned bits (fond) from the bottom. Simmer for 3 minutes to reduce slightly.
Add the chicken broth and bring to a gentle simmer.
Return the chicken thighs to the pan, skin-side up. Ensure the skin remains above the liquid level to stay crispy.
Reduce heat to low, cover partially, and braise for 20-25 minutes, or until the internal temperature reaches 165°F (74°C).
Optional: Remove chicken, whisk butter into the sauce to thicken, then serve sauce spooned around the chicken (not over the skin).