Season your beef tenderloin generously with salt and pepper on all sides. Heat olive oil in a large skillet over high heat until it is shimmering. Sear the beef quickly for about 2 to 3 minutes per side until a brown crust forms, but the inside remains raw. Remove the beef from the pan and immediately brush it all over with the spicy mustard while it is still warm, then set it aside to cool completely.
In the same skillet, melt the butter over medium heat. Add the finely chopped mushrooms, shallots, garlic, and thyme. Cook the mixture, stirring frequently, until all the moisture released by the mushrooms has evaporated and you are left with a thick, concentrated paste. This process can take about 10 to 15 minutes. Season with a pinch of salt and pepper, then let the mixture cool to room temperature.
Lay out a large piece of plastic wrap on your counter. Arrange the turkey bacon slices in a slightly overlapping rectangle that is large enough to wrap around the beef. Spread the cooled mushroom mixture evenly over the turkey bacon. Place the seared beef at one end and, using the plastic wrap to help you, roll the beef tightly inside the turkey bacon and mushroom layer. Twist the ends of the plastic wrap to form a tight log and refrigerate for at least 20 minutes to firm up.
Preheat your oven to 400 degrees Fahrenheit. On a lightly floured surface, roll out the puff pastry into a rectangle large enough to enclose the beef log. Remove the beef from the plastic wrap and place it in the center of the pastry. Brush the edges of the pastry with egg wash, then fold the pastry over the beef, sealing the seams tightly. Place the log seam-side down on a parchment-lined baking sheet and brush the entire exterior with egg wash.
Use a sharp knife to gently score a decorative pattern on top of the pastry, being careful not to cut all the way through. Bake for 25 to 30 minutes or until the pastry is deep golden brown and the internal temperature of the beef reaches 130 degrees Fahrenheit for medium-rare. Let the Easy Beef Wellington rest for at least 10 minutes before slicing into thick rounds to serve.
