Spread coarsely cracked peppercorns onto a plate and firmly press each steak into the peppercorns, coating both sides evenly. Sprinkle salt generously onto both sides of the steaks, then set aside.
Melt 1 tbsp of butter in a skillet over medium-high heat. Once melted, add the steaks. Cook for about three minutes, then flip the steaks carefully, cooking for another 3 minutes, or until your liking. Remove the steaks from the skillet. Place the steaks onto a dish, and loosely cover with a piece of parchment paper.
Reduce the heat to medium. Into the same skillet, add remaining 3 tbsp butter and melt. Add in the shallot. Sauté for a minute, then add in the garlic. Stir and cook for another minute. Add in the mushrooms and 1/2 tsp of salt. Cook until the shallots are caramelized and the mushrooms are soft.
Add in the broth, heavy cream, dijon mustard, and Worcestershire. Stir to combine and allow the sauce to simmer, stirring often, until thick enough to coat the back of a spoon.
Spoon over peppercorn steak, and serve. Store leftovers in an airtight container in the fridge for up to 3-4 days.