Finely mince the mushrooms, shallots, and garlic, then sauté in a dry pan over medium heat until all moisture has evaporated and the mixture is concentrated.
Season the beef tenderloin with sea salt and black pepper on all sides.
Heat avocado oil in a cast-iron skillet over high heat and sear the beef for 1 minute per side until a brown crust forms, then remove from heat.
Immediately brush the warm beef with Dijon mustard and set aside to rest.
Lay a sheet of plastic wrap on a flat surface, place the prosciutto slice down, and spread the mushroom duxelles and thyme evenly over the prosciutto.
Place the beef in the center of the mushrooms and roll the prosciutto tightly around the beef using the plastic wrap, then chill in the freezer for 10 minutes to firm up.
Roll out the puff pastry on a lightly floured surface, unwrap the beef, and place it in the center of the pastry.
Fold the pastry over the beef, sealing the edges with a bit of whisked egg, and trim any excess dough.
Place the Wellington on a parchment-lined baking sheet, brush the entire exterior with the remaining egg wash, and bake at 425°F for 15-20 minutes until the pastry is golden brown.