Preheat the oven to 425°F. Place the pastry on the counter to take the chill off.
Heat a small skillet over medium heat. Add 1 tablespoon of EVOO (1 turn of the pan) and the butter. When the butter melts into the EVOO, add the shallot, mushrooms and thyme. Cook for 4 to 5 minutes, then season with salt and pepper; add the sherry.
Cook off the liquid until dry, about 1 minute. Remove from the heat, reserve and let cool.
Heat a large nonstick skillet over high heat. Drizzle EVOO over the meat to lightly coat it on both sides. Place the meat in the hot skillet and sear to caramelize, 2 minutes on each side. (Don't move the meat while cooking it.) Remove the meat after 4 minutes and let it cool completely. Pat the steaks dry and season with salt and pepper just before wrapping in the dough.
Cut the pâté evenly into 4 flat 2-ounce portions. Cover a baking sheet with parchment paper.
Open the puff pastry dough on the parchment paper. Quarter the dough with a sharp knife.
On 1 rectangle, mound one-fourth of the cooked mushrooms. Top the mushrooms with a portion of pâté and a beef tournedo. Brush the edges of the dough with egg wash. Wrap the dough up and over the meat, sealing it with egg wash and tucking in the ends as you would a wrapped present. Repeat and arrange the 4 Wellingtons on a baking sheet. Brush the completed Wellingtons with egg wash and bake until golden, 12 to 15 minutes.
Remove the meat from the oven and let rest for 5 minutes. Plate the beef Wellingtons individually with a few broccoli spears and half of a broiled tomato alongside.