Pound each chicken breast between plastic wrap to an even 1/2-inch (1.3cm) thickness, pat completely dry, season both sides with kosher salt, and press most of the cracked peppercorns firmly into both sides, reserving about 1 teaspoon for the sauce.
Heat olive oil and 1 tablespoon butter in a skillet over medium-high until butter foams and oil shimmers, then sear chicken in a single layer for 4 to 5 minutes per side until deep golden and internal temperature reaches 160°F (71°C). Transfer to a plate and tent with foil.
Lower heat to medium and add 2 tablespoons butter to the same skillet, then cook minced shallots for 2 minutes until softened and translucent before stirring in garlic for 30 seconds until fragrant.
Pull the skillet off the heat, pour in Cognac or brandy, return to heat, and scrape the bottom of the pan with a wooden spoon to lift all the browned fond, letting it simmer for about 1 minute until slightly reduced and the sharp alcohol smell cooks off.
Pour in beef stock and bring to a simmer, reducing by about half over 3 to 4 minutes, then stir in heavy cream, Dijon mustard, thyme sprigs, and reserved cracked peppercorns, simmering gently for 4 to 5 minutes until the sauce coats the back of a spoon.
Remove thyme sprigs, return chicken and any resting juices to the skillet, spoon sauce over the chicken and let everything warm together for 2 minutes while basting the tops, then scatter chopped parsley over the top and serve immediately.