Preheat the oven to 400°F (200°C). Pat the chicken thighs completely dry with paper towels—this is crucial for crispy skin. Season both sides generously with salt and pepper.
Heat the olive oil in a large oven-safe skillet (preferably cast iron) over medium-high heat. Once shimmering, place the thighs skin-side down and cook undisturbed for 6–7 minutes until the skin is deep golden brown and releases easily. Flip and sear the other side for 2 minutes.
Transfer the skillet to the preheated oven. Roast for 20–25 minutes, or until an instant-read thermometer inserted into the thickest part registers 165°F (74°C). Remove from oven and transfer chicken to a plate, loosely tent with foil.
Pour off all but 1 tablespoon of fat from the skillet. Return to medium heat, add garlic, rosemary, and thyme. Sauté for 30 seconds until fragrant. Add butter (or alternative), chicken broth, and lemon juice. Bring to a simmer, scraping up any browned bits. Whisk in the cornstarch slurry and simmer until the sauce thickens, about 1–2 minutes.
Return the chicken thighs to the skillet, spoon sauce over the top, and let them warm through for a minute. Arrange on a platter, drizzle with remaining sauce, and garnish with extra fresh herbs.