Dry the chicken thighs with paper towels. In a large bowl or resealable bag, combine chicken with 2 tablespoons olive oil, lemon pepper seasoning, garlic powder, and dried parsley. Massage the mixture into the chicken evenly, then cover or seal and chill for at least 1 hour or overnight for best flavor infusion.
Heat a large skillet on medium and add butter plus 1 tablespoon olive oil. Once shimmering, place about half the chicken thighs skin-side down carefully and cook without moving until skin turns golden brown, about 3 to 4 minutes. Flip and cook the other side for 2 to 3 minutes more, then transfer the browned chicken to a plate. Repeat with the remaining thighs.
Add the whole garlic cloves to the skillet and sauté frequently, stirring gently until they soften and develop a golden color, about 2 to 3 minutes.
Pour in chicken broth to deglaze the pan, scraping up browned bits with a wooden spoon. Let simmer briefly for 1 to 2 minutes. Stir in the heavy cream and fresh lemon juice, mixing well to combine. Bring the sauce up to a gentle boil, stirring occasionally. Add capers and stir to blend their flavor throughout the sauce.
Return the browned chicken pieces to the pan, skin side up if possible, and spoon sauce over each piece. Lower heat to medium-low and simmer gently for 15 to 20 minutes, allowing the sauce to thicken and the chicken to cook completely (internal temperature should reach 165°F).
Serve the chicken thighs smothered in the creamy lemon garlic caper sauce with your favorite sides such as mashed potatoes or rice. Enjoy your easy and delicious family dinner!