Prep the chicken: Pat the chicken dry with a paper towel. Season both sides with salt and pepper.
Cook the chicken: Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5–6 minutes per side until golden and fully cooked. Remove from skillet and set aside.
Make the sauce: Lower heat to medium. Melt butter in the same skillet and sauté garlic for 30 seconds. Add heavy cream, parmesan, lemon juice, lemon zest, and thyme. Stir until slightly thickened, about 3–4 minutes.
Combine chicken and sauce: Return chicken to the pan and spoon sauce over the pieces. Let simmer for 1–2 minutes to let flavors meld.
Serve: Plate chicken, drizzle extra sauce on top, and sprinkle with parsley. Serve with zucchini noodles, cauliflower rice, or a salad.