Heat a skillet on medium-low heat and place the chicken thighs skin-side down in the pan.
Add 1 tablespoon of olive oil to help the skin crisp up, then cook until golden brown.
Remove the chicken, add remaining olive oil and butter to the pan.
Add garlic and sauté until aromatic, then pour in chicken broth and sprinkle with cayenne pepper.
Return the chicken thighs to the skillet and simmer briefly to absorb flavors.
Adjust seasonings with salt and pepper as needed, then sprinkle with parsley.
Serve warm with lemon wedges on the side for added brightness.