For the sauce

1. Make sauce. In a small saucepan, bring beef broth and Madeira wine to a boil over medium-high heat. Continue to simmer mixture until reduced to 1 cup, about 15-20 minutes. Season to taste with salt and pepper. Set aside.

For the tarts

1. Cook mushrooms. Heat butter in a small skillet over medium-low heat; add shallots and cook, stirring frequently, until softened, 3-5 minutes. Stir in mushrooms, increase heat to medium-high, and cook, stirring frequently, until most of liquid given off by mushrooms has evaporated, 7-10 minutes. Add cream, Madeira wine, salt, and pepper; cook until mixture is mostly dry, 2-3 minutes longer. Remove from heat and stir in thyme. Set aside.
2. Prep oven. Heat oven to 350 degrees F.
3. Prep puff pastry. Unfold one sheet of puff pastry and cut it in half. Cut one of the halves in half again to make two small squares of puff pastry. Save remaining puff pastry (uncut half) for another use. Place puff pastry squares on a baking sheet lined with parchment paper. With the tip of a sharp paring knife, lightly score a border on each puff pastry square 1/2 inch from edges (being careful not to cut all the way through the puff pastry).
4. Add pâté and mushrooms. Spread half of pâté mousse on each puff pastry square up to the scored border line. Spread mushroom mixture on top of the pâté mousse equally dividing mushrooms between the two squares. Brush the borders with the egg wash, if desired.
5. Bake. Bake tarts for 15-20 minutes, until the pastry is lightly browned and the sides have puffed up. Let cool while the beef cooks.

For the beef

1. Prep. Heat oven to 450 degrees F.
2. Sear beef. Rub each steak all over with 1/2 teaspoon oil and season generously with salt and pepper. Heat a 10-inch heavy-bottomed oven proof skillet (preferably cast iron) over high heat on stovetop until very hot, about 3 minutes. Place steaks in skillet and cook, without moving steaks, until well-browned and a nice crust has formed on the underside, about 3 minutes. Turn steaks with tongs and cook until well-browned and a nice crust has formed on second side, about 3 minutes longer. Sear edges until well-browned.
3. Finish beef. Transfer skillet to oven and roast until internal temperature reaches 120 degrees for rare (4 to 6 minutes), 125 degrees for medium-rare (6 to 8 minutes), or 135 to 140 degrees for medium (8 to 10 minutes). Transfer steaks to cutting board; loosely tent with foil, and let rest about 5 minutes before slicing.

For assembly

1. Warm sauce. While beef rests, re-warm sauce over low heat. Then whisk in butter until incorporated.
2. Serve. Slice beef across the grain and place slices on top of each tart. Drizzle a little sauce on top of each tart. Serve remaining sauce at the table.