Heat olive oil in a large skillet over medium heat-high.
Add the chicken and cook approximately 5 minutes on each side, until browned on all sides. Transfer to a plate and set aside.
Add the butter and shallots to the pan. Cook, stirring regularly, until the butter has melted and the shallots have softened, about 1-2 minutes.
Pour in the broth and use a wooden spoon to deglaze the pan, gently scraping up any browned bits at the bottom of the pan.
Pour in the heavy cream then add the thyme sprigs and cracked black pepper. Stir and cook together for about 1 minute.
Add the chicken back to the pan and cook for about 5 more minutes, turning the chicken over and basting with the sauce throughout this time. You'll want to do this just until the chicken is cooked thoroughly, when a meat thermometer reads an internal temperature of 165°F for each piece of chicken.
Remove fully cooked chicken from the pan and transfer to a plate. Also remove the thyme sprigs from the pan and discard those.
Add the lemon juice to the remaining sauce in the pan. Stir, and allow the sauce to bubble up and thicken for 2-3 minutes (see Notes for additional thickening tips).
Place chicken onto serving plates. Pour sauce over each serving and sprinkle with chopped parsley. Serve with a lemon wedge.
Notes
Makes approximately 4 servings.
If you have whole peppercorns, you can use a mortar and pestle to gently crush them. Or, place them into your pepper grinder and grind them on the largest setting.
Make it dairy free: use your favorite non-dairy heavy cream and plant-based butter.
Use freshly squeezed lemon juice if you can; the store-bought lemon juice in those lemon-shaped containers do not have the same flavor and will alter the flavor of the final dish.