Pat the steaks dry and season generously with kosher salt on all sides. Place them on a wire rack set over a rimmed baking sheet and let them air-dry in the refrigerator for about 30 minutes, uncovered, to develop a dry surface.

While the steaks rest, crack the peppercorns into coarse chunks. You can do this with a pepper mill on its coarsest setting, a mortar and pestle (carefully, as some might jump out), or, for best results, use a heavy object like a meat pounder, skillet, or large mallet. Wrap the peppercorns in a kitchen towel to keep them contained while crushing.

Preheat your oven to 375°F (190°C). Spread the crushed peppercorns on a plate and press one side of each steak into the pepper to coat it in an even layer. Set the steaks aside with the peppercorn crust facing up. If any peppercorns remain, reserve them. If needed, crush more to ensure all steaks are properly coated.

In a large stainless steel or cast iron skillet, heat the vegetable oil over medium-high heat until it shimmers. Place the steaks, peppercorn side down, into the skillet. Cook for about 3 minutes until the peppercorns are fragrant and toasted. Carefully flip the steaks, ensuring the pepper crust stays intact. Add the butter, thyme sprigs, and garlic, then baste the steaks with the melted butter using a spoon as they sear on the other side. Remove the pan from the heat once the steaks are seared.

Transfer the steaks to a rimmed baking sheet. Use an instant-read thermometer to check the internal temperature; if it reaches 125°F (52°C), the steaks are medium-rare. If not, transfer them to the preheated oven and cook until they reach the desired doneness based on their thickness. Once the target temperature is achieved, let the steaks rest for about 5 minutes.

Remove all but 1 tablespoon of fat from the skillet, discarding the garlic and thyme. Add the minced shallot and any remaining cracked peppercorns. Cook over medium heat, stirring until the shallot softens, approximately 2 minutes.

Turn off the burner if using a gas stove to add the brandy or cognac safely. Then, re-ignite the burner and cook until the alcohol's raw scent dissipates, and the liquid reduces almost completely.

Pour in the chicken stock, scraping up the browned bits on the pan's surface, and bring the mixture to a simmer. Stir in the heavy cream or crème fraîche and whisk continuously until the sauce thickens enough to coat the back of a spoon. Add the Dijon mustard, whisking until well combined. Season the sauce to taste with a pinch of salt.

Place the rested steaks on plates and pour the sauce generously over each piece. Serve alongside French fries, creamy mashed potatoes, or any side of your preference.