Using a mortar and pestle, roughly crack peppercorns. You can also place peppercorns in a zip-top bag and crush them with a mallet or bottom of a saucepan.
In a large skillet, heat oil over medium heat. Season chicken with salt, then brown the chicken on both sides, working batches to avoid overcrowding the pan. Chicken will take about 5 minutes per side. Remove chicken to a plate and set aside.
Add butter and shallot to the skillet and cook until shallot is soft, 1-2 minutes. Stir in broth, heavy cream, thyme, and the cracked peppercorns. Cook 1-2 minutes, scraping any stuck on bits from the bottom of the pan.
Nestle chicken back into the pan along with any accumulated juices, then bring to a simmer, occasionally basting with the sauce, until chicken has cooked through, 6-8 minutes. (Chicken should read 165°F in the thickest part of the thigh.)
Remove chicken to serving plates and throw away thyme sprigs.
Stir lemon juice into skillet and cook until sauce has thickened slightly, about 2 minutes. Season to taste with salt and stir in parsley.
Spoon sauce over chicken and serve. Enjoy!
