Pound the chicken: Place each chicken breast between sheets of plastic wrap and pound with a meat mallet to an even 1/2-inch thickness. This helps the chicken cook through evenly without drying out the edges.
Press on the pepper crust: Sprinkle both sides of the chicken with kosher salt, then press the cracked peppercorns firmly into the surface with your hands. Let the chicken sit for a few minutes so the crust adheres while you heat the pan.
Heat the skillet: Melt 1 tablespoon of the butter with the olive oil in a large skillet over medium-high heat until it shimmers. A hot pan is key to building a deep, dark crust on the pepper coating.
Sear the chicken: Add the chicken and sear for 4 to 5 minutes per side, until a deep golden crust forms and a meat thermometer inserted in the thickest part reads 165°F. Avoid moving the chicken too soon so the crust can set.
Rest the chicken: Transfer the chicken to a plate and tent loosely with foil. Resting keeps the juices inside the chicken while you build the sauce in the same pan.
Sauté the garlic: Lower the heat to medium and add the minced garlic to the skillet, stirring for about 30 seconds until fragrant. Watch closely so it doesn't scorch and turn bitter.
Deglaze the pan: Pour in the chicken broth and scrape up the browned bits stuck to the bottom of the skillet with a wooden spoon. These bits carry most of the flavor for the sauce.
Whisk in mustard: Stir in the Dijon mustard until it dissolves into the broth, creating a tangy base. Let the mixture simmer for about 1 minute to reduce slightly.
Add the cream: Pour in the heavy cream and whisk to combine. Simmer over medium-low heat, stirring occasionally, until the sauce thickens enough to coat the back of a spoon, about 4 minutes.
Return the chicken: Nestle the chicken back into the skillet along with any juices from the plate. Spoon the sauce over the top and simmer gently for 2 minutes to warm the chicken through.
Finish with thyme: Stir in the fresh thyme leaves and the remaining 1 tablespoon of butter off the heat, swirling the pan until the butter melts into the sauce. This gives the sauce a glossy finish.
Serve: Plate the chicken and spoon extra sauce over the top, garnishing with a few more thyme leaves. Serve immediately while the sauce is warm and the crust is still crisp.