Preheat oven to 400°F and finely mince the mushrooms and garlic.
Sauté the mushrooms, garlic, and thyme in a dry pan over medium heat until all moisture has evaporated and the mixture is concentrated.
Season the beef with salt and pepper, then sear in olive oil in a hot pan for 1-2 minutes per side until browned.
Remove the beef from the pan and immediately brush all sides with Dijon mustard while warm.
Lay out a piece of plastic wrap, arrange the prosciutto slices in an overlapping rectangle, and spread the mushroom duxelles evenly over the prosciutto.
Place the beef in the center, roll tightly using the plastic wrap to form a log, and chill in the freezer for 10 minutes to set the shape.
Remove plastic, wrap the beef log in the puff pastry, seal the seams, brush with egg yolk, and bake for 20-25 minutes until the pastry is golden.