Season and dredge the chicken breasts in a mixture of flour, salt, and pepper, ensuring even coating for a golden crust.
Heat 2 tablespoons of butter and olive oil in a large skillet over medium-high heat. Once the butter begins to foam, add your chicken. Sear for 4-5 minutes per side until golden brown.
Lower the heat and add the remaining butter and garlic to the same pan. Sauté until fragrant, about 30 seconds.
Pour in the chicken broth, scraping the bottom of the pan to incorporate all those flavorful bits. Add heavy cream, lemon juice, and zest, stirring continuously. Let it simmer for 3-4 minutes until it begins to thicken.
Return the chicken to the pan, nestling it into the sauce. Add thyme and simmer for another 5-7 minutes until the chicken reaches 165°F internally and the sauce has reduced by approximately one-third. Spoon the sauce over the chicken periodically.
Garnish with fresh parsley and lemon slices before serving.