Place the top oven rack in the center position and pre-heat the oven to 400°F.
Heat two tablespoons olive oil in a large, high-sided skillet over medium heat. Add the leeks, mushrooms, and garlic. Season with salt and black pepper, to taste, and stir to combine.
Cook, stirring occasionally, until the vegetables develop some color and most of the water from the mushrooms evaporates, approximately 8-10 minutes.
Add the spinach and fresh herbs. Continue cooking until the spinach wilts, approximately 1-2 minutes. Remove from heat and set aside.
Place the butterflied beef tenderloin between two sheets of plastic wrap or wax paper and gently pound with a meat mallet or rolling pin to a½-inch even thickness. Brush the surface of the beef with the remaining olive oil and generously season with salt and black pepper, to taste.
Stir the Parmesan cheese into the mushroom-spinach mixture until combined. Evenly spread the mixture over the beef tenderloin, leaving a small border (½-1 inch) around the edges.
Carefully roll up the tenderloin like a jelly roll and secure with kitchen twine. Season the outside of the beef with additional salt and black pepper,as desired, and place in the center of a roasting pan lined with the sliced red onions.
Nestle the shallots and carrots around the beef and tuck in the fresh thyme sprigs. Add the beef broth and place in the pre-heated oven to roast until the beef reads between 125°F-130°F*for medium-rare on an instant read thermometer, approximately 35-40 minutes. (The temperature will rise another 5-10 degrees while resting).
Transfer the beef tenderloin to a serving platter and cover loosely with foil to keep warm. If necessary, return the vegetables to the oven for another 10-15 minutes, or until fork tender.
Transfer the veggies to the serving platter and pour the pan juices into a medium sauce pan. Place over medium-high heat and reduce for approximately 5 minutes, stirring occasionally. Add the butter and stir to emulsify the butter and thicken the sauce.
Carve the stuffed tenderloin and serve immediately with the roasted vegetables and pan sauce. Enjoy!