Preheat your oven to 425°F (220°C). In a large bowl, toss the potato wedges with olive oil, minced garlic, paprika, salt, and pepper until well coated. Spread the wedges in a single layer on a baking sheet. Bake for 30-35 minutes, flipping halfway through, until golden and crispy. In the last 5 minutes of baking, sprinkle the Parmesan cheese over the fries and return to the oven until melted.

Season the filet mignon steaks generously with salt and black pepper. In a large skillet, heat the butter over medium-high heat until melted and bubbly. Add the steaks to the skillet and sear for 4-5 minutes on each side for medium-rare, or until desired doneness is achieved. In the last minute of cooking, sprinkle the chopped chives over the steaks. Remove from heat and let rest for a few minutes.

In a separate skillet, heat olive oil over medium heat. Add the sliced mushrooms and cook until they are browned and tender, about 5-7 minutes. Stir in the minced garlic and cook for another minute until fragrant. Pour in the heavy cream and beef broth, and stir to combine. Allow the sauce to simmer for 5-7 minutes until slightly thickened. Season with salt and pepper to taste.

Plate the filet mignon and spoon the creamy mushroom sauce over the top. Serve with garlic-Parmesan wedge fries on the side, garnished with fresh parsley and thyme if desired.