Prepare and Season Steaks: Generously coat the beef tenderloins on all sides with kosher salt, allow to stand at room temperature for 45 minutes-2 hours.
Preheat Oven and Crack Peppercorns: Preheat oven to 325F. Crack peppercorns in a mortar and pestle until all the berries are at least halved - shake in a fine mesh sieve to filter out the fine grinds. Pack the top and bottom of each steak with coarse peppercorns.
Cook Steaks: In a medium nonstick pan, heat vegetable oil until almost smoking. Press steaks into oil and cook for 1-3 minutes per side, until the peppercorns are deeply toasted but not burnt. Transfer to a wire rack set in a rimmed baking sheet and finish in the 325F oven to desired doneness. Wrap in aluminum foil and allow to rest at least 5 minutes before serving.
Make Peppercorn Cream Sauce: Melt butter in a medium stainless sauté pan over medium heat, until foaming subsides. Add shallot and sauté, tossing frequently for 1-3 minutes, until translucent. Add 2-3 tablespoons of peppercorns and toast for 30 seconds. Remove pan from the heat, add brandy, and flame if desired. Return the pan to the burner, add beef stock and simmer until reduced by 75% (if using demi glace, reduce by 50%). Add cream and simmer until smooth and thick.
Fry Eggs: In a medium nonstick pan, melt butter until foaming subsides. Fry eggs sunny-side up in one side of the pan so they form a half-circle.
Carve Steak and Serve: Carve the steak and serve with the eggs, drizzle with peppercorn sauce.