Pat chicken thighs dry with a paper towel. Place in a large resealable bag or bowl with 2 tablespoons olive oil, lemon pepper seasoning, garlic powder, and dried parsley. Massage spices into chicken until fully coated. Seal and refrigerate for at least 1 hour or up to overnight.

Heat a large skillet over medium heat. Add butter and remaining 1 tablespoon olive oil. Once hot and foamy, add chicken thighs skin-side down in batches of 3. Brown undisturbed for 3 to 4 minutes until golden, then flip and cook another 2 to 3 minutes. Transfer to a clean plate and repeat with remaining thighs. Chicken will not be fully cooked through at this stage.

Add whole garlic cloves to the same skillet. Stir often and cook for 2 to 3 minutes until softened and lightly golden. Watch closely to avoid burning.

Pour in chicken broth and scrape up all browned bits from the bottom of the pan with a wooden spoon. Let simmer 1 to 2 minutes. Add heavy cream and lemon juice, stir well, and bring to a gentle boil. Stir in the capers.

Return the browned chicken thighs to the skillet and spoon sauce over the top. Reduce heat to medium-low, cover loosely, and cook for 15 to 20 minutes until sauce thickens and chicken registers 165°F on a meat thermometer.

Spoon the creamy lemon garlic caper sauce generously over the thighs and serve hot alongside your favorite sides.