Preheat oven to 400F.
Heat a saucepan with the butter, balsamic vinegar over medium heat. When the balsamic begins to bubble, turn the heat down to medium-low and cook for 3 minutes to reduce to half. Add in the red wine and the beef broth and let simmer for 5-8 minutes until reduces to a sauce thick enough to coat back of spoon. Taste and season with salt.
Place the peppercorns in a baking sheet. Use a heavy bottomed skillet to gently crush the peppercorns by pressing the bottom of the skillet on top of the peppercorns using a rocking motion.
Rub each filet mignon lightly with the cooking oil. Season each filet mignon with salt on both sides and then press the filet mignon onto the peppercorns on both sides.
Heat large oven-proof skilling on high heat. When very hot, add the filet mignon, searing both sides for 1 minute each. Remove the filet mignon from the heat and onto the baking sheet (it’s okay if there’s still peppercorn on the baking sheet). Place into oven for 4-7 minutes, depending on your desired doneness and thickness of filet mignon.
For 1-inch filet mignon: 4 minutes and then check temperature with meat thermometer. For every ¼” more, add 1 minute.Rare: 120F-125FMedium-Rare: 130F-135FMedium: 140F-145F
Let rest for 3 minutes before serving with the Balsamic Sauce.