Season the chicken breasts with salt and pepper, then dredge them in flour.
Heat 1 tablespoon of butter and 1 tablespoon of olive oil in a large skillet over medium-high heat.
Add the dredged chicken breasts to the skillet and cook for 4–6 minutes per side, or until they’re cooked through and lightly browned. Check that the internal temperature has reached 165°F using a meat thermometer. Transfer the chicken to a plate, cover, and set aside to rest.
Add the remaining butter and oil to the skillet, then stir in the minced garlic. Cook for about 30 seconds, just until the garlic is fragrant.
Pour in the broth and scrape up any browned bits from the bottom of the pan. Whisk in the lemon juice, heavy cream, and ground thyme.
Season with salt and pepper to taste. Let the sauce simmer for 2–3 minutes, or until slightly thickened.
Return the chicken to the pan along with the lemon slices, and spoon the sauce over the top. Remove from heat and garnish with parsley.
