Pound the chicken: Place chicken breasts between plastic wrap and pound to an even 1/2-inch thickness. This helps them cook evenly and stay tender.
Season with pepper: Sprinkle salt over both sides of the chicken, then press the cracked peppercorns firmly into the surface so they stick well.
Sear the chicken: Melt 2 tablespoons butter in a heavy skillet over medium-high heat. Sear the chicken about 4 minutes per side until a deep brown crust forms, then transfer to a plate.
Rest the chicken: Let the seared chicken rest for 5 minutes while you build the sauce. This keeps the juices inside the meat.
Deglaze the pan: Pour the chicken broth into the same skillet, scraping up the browned bits from the bottom with a wooden spoon, about 1 minute.
Build the sauce: Whisk in the heavy cream, Dijon mustard and soy sauce mixture. Simmer for 3-4 minutes until the sauce thickens slightly.
Return the chicken: Slide the chicken back into the sauce and spoon it over the top to warm through for 2 minutes.
Cook the vegetables: In a separate skillet, melt the remaining 2 tablespoons butter over medium-high heat. Add the vegetables and garlic, tossing often, until tender-crisp and lightly browned at the edges, about 6-8 minutes.
Plate and garnish: Arrange the chicken and sauce alongside the buttery vegetables. Sprinkle with chopped parsley before serving.