Season the beef tenderloin evenly with salt and black pepper.
Heat olive oil in a skillet over medium-high heat. Sear the beef on all sides until browned, about 2 minutes per side. Remove from heat and let cool slightly.
In the same skillet, melt butter over medium heat. Add minced garlic and shallot, sauté for 2 minutes until fragrant.
Add finely chopped mushrooms to the skillet. Cook, stirring frequently, until the mushrooms release their moisture and it evaporates, about 8-10 minutes.
Pour in the white wine and cook until the liquid has mostly evaporated, about 3 minutes.
Remove from heat and stir in fresh thyme leaves and chopped parsley. Let the mushroom mixture cool completely.
Brush the seared beef with Dijon mustard on all sides.
Roll out the thawed puff pastry on a lightly floured surface to a rectangle large enough to wrap the beef completely.
Spread the cooled mushroom mixture evenly over the puff pastry, leaving a 1-inch border around the edges.
Place the beef in the center of the mushroom-covered pastry.
Fold the pastry over the beef, sealing all edges by pressing firmly. Trim any excess pastry if needed.
Brush the outside of the pastry with the beaten egg to help seal and give a golden finish.
Place the wrapped beef seam-side down in the slow cooker.
Cover and cook on low for 3 to 3.5 hours, or until the beef reaches your desired doneness (medium-rare is recommended).
Carefully remove the Beef Wellington from the slow cooker and let it rest for 10 minutes before slicing and serving.