Clean the mushrooms if necessary using a paper towel, towel or brush. Finely chop the mushrooms, garlic and shallots with a chef knife or add to a food processor and pulse until finely chopped. Do not let the food processor run continuously.
Heat a saute pan over medium heat. Add the butter. Saute the shallot mixture until translucent. Add the mushrooms and cook until most of the liquid has evaporated and mushrooms are caramelized. Keep a close eye on the mushrooms and don't allow them to burn. Throughout the process as the mushrooms caramelize, gradually add the sherry. Allow the liquid to evaporate. The mushrooms should appear dry. Mix in the fresh thyme leaves and set aside to cool. When cooled to room temperature, place in bowl and refrigerate.
Using butcher's twine, tie the tenderloin in multiple areas to create a more even cylindrical shape. This will allow for a more even cook and help the meat keep the proper shape.
Pat the surface of the meat dry with a paper towel if wet. Lightly coat entire surface with oil. Lightly salt the beef.
Preheat large skillet to medium-high heat.
Quickly sear all sides of the beef including the ends. NOTE: You are only searing the meat not cooking it at this point.
Remove beef from skillet. Cool to room temperature. Remove butcher's twine from the beef. When cool, place beef in refrigerator covered with plastic wrap to chill.
Lay out multiple overlapping pieces of plastic wrap approximately 2 feet long on your countertop. Lay down approximately 14 overlapping pieces of prosciutto being careful not to rip the slices.
Remove the duxelles from refrigerator. Place onto the prosciutto layer, an even rectangle of duxelles that is wide enough to extend an inch or so beyond the ends of the tenderloin.
Remove the beef tenderloin from the refrigerator and coat it in dijon mustard. Place the tenderloin in the center of the duxelles. Use the plastic wrap to gently lift the prosciutto up and over the beef tenderloin. You want to wrap it as tight as possible in the plastic wrap to form an even log shape. Twist the ends of the plastic and secure. Place in the refrigerator to chill.
Lightly flour your countertop with white flour. Unwrap your chilled dough. If it is too rigid, allow pastry to warm up slightly until it is pliable.
Either working on a silicone mat, or on overlapping plastic wrap, unwrap the tenderloin and place it onto the rolled out pastry dough. Roll up the tenderloin in the puff pastry lengthwise first.
At the seam where the dough meets to seal up, brush one side of the dough at the seam with some of the egg wash. Press the dough together completely to form a tight seal and fold under if excess dough.
If not doing a lattice top, brush the top of the Wellington with egg wash and it is ready to bake. Sprinkle dough with a bit of kosher salt after brushing with egg wash.
Preheat oven to 425°F. Set up a rack about ⅓ up from the bottom of the oven.
Lightly spray a small sheet pan with baking spray and place prepared Wellington on pan.
Bake until the Wellington reads 105-110°F with a cooking alarm thermometer that you leave in the beef while cooking or when it registers 105-110°F with an instant read thermometer.
Remove the Wellington from the oven and rest uncovered for at minimum 20 minutes. Do not remove the temperature probe from the meat during the rest.
Slice the Beef Wellington into at least 1 inch slices and serve immediately.
