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Add peppercorns to a zippered food storage bag and seal. Lightly pound with a meat mallet or skillet until peppercorns are broken and cracked. Set aside.
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Add olive oil and 1 tablespoon butter to a 12-inch nonstick skillet set over medium heat. Heat until the butter is melted and no longer bubbling. Swirl the pan to combine oil and butter.
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Season the chicken with salt and add to the skillet. Cook chicken on both sides until lightly browned, about 3 to 4 minutes per side. Remove to a plate and keep warm.
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Add remaining butter and shallot to the skillet. Cook, stirring, until butter melts and shallot is softened, about 1 minute.
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Stir in broth, heavy cream, thyme, and cracked peppercorns. Cook, stirring, and bring to a boil. Make sure to stir up any browned bits that are left into the sauce from the bottom of the pan.
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Add chicken and any juices from the plate. Return to a boil, then reduce to a simmer. Cook until chicken is no longer pink at the center and juices run clear, 8 to 10 minutes. An instant read thermometer inserted into the thickest part should read 165 degrees F (74 degrees C).
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Divide chicken among 4 plates over rice. Turn the heat back to medium, add lemon juice, and cook until sauce thickens and darkens a bit, 3 to 5 minutes.
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Spoon sauce over chicken and garnish with parsley.