Place chicken breasts between two pieces of plastic wrap and pound to an even 0.5-inch thickness. This helps them cook evenly. Season both sides generously with salt and black pepper.

Heat olive oil in a large skillet over medium-high heat. Once shimmering, add the seasoned chicken breasts. Sear for 4-6 minutes per side, until golden brown and cooked through (internal temperature reaches 165°F). Remove chicken from the skillet and set aside on a plate, tented loosely with foil.

Reduce heat to medium. Add butter to the same skillet, scraping up any browned bits from the chicken. Add minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.

Pour in the chicken broth, scraping the bottom of the pan again to release any flavorful fond. Bring to a simmer and let it reduce slightly, about 2-3 minutes.

Stir in the heavy cream, lemon juice, chopped fresh parsley, and thyme. Bring the sauce to a gentle simmer and cook for 3-5 minutes, stirring occasionally, until it thickens slightly to your desired consistency.

Return the seared chicken breasts to the skillet, spooning the creamy sauce over them. Let them warm through in the sauce for 1-2 minutes. Garnish with extra fresh parsley if desired. Serve immediately.