Preheat the oven to 400°F (200°C).
Heat a drizzle of olive oil and a pat of butter in a large oven-safe skillet over medium heat until the butter melts.
Add the peeled garlic cloves and cook, turning occasionally, until lightly browned, about 3–5 minutes; transfer the garlic to a plate but leave the flavored oil and butter in the pan.
Pat the chicken thighs dry with paper towels and season both sides generously with salt and pepper.
Increase the heat to medium-high and place the chicken thighs skin-side down in the skillet; cook, without moving, until the skin is browned, about 5–6 minutes, then remove the skillet from the heat.
Season the chicken with about 1 tsp each of chopped fresh thyme and rosemary, flip so the skin side is up, and sprinkle another 1 tsp each of thyme and rosemary over the exposed side.
Scatter the browned garlic cloves around the chicken, then transfer the skillet to the preheated oven and roast until the skin is crispy and an instant-read thermometer inserted into the thickest part reads 165°F (74°C), about 20 minutes.
Remove the chicken and garlic to a plate. Place the skillet with the drippings over medium heat and bring to a simmer.
In a small bowl, whisk together chicken broth and a small amount of cornstarch to make a slurry, then whisk the slurry into the simmering drippings; cook, whisking, until slightly thickened, about 1 minute.
Remove the pan sauce from the heat and stir in the lemon juice.
Spoon some pan sauce onto each plate, top with a roasted chicken thigh and several garlic cloves, and sprinkle with chopped fresh parsley before serving.