Preheat your oven to 425°F (220°C). In a large bowl, toss the potato wedges with olive oil, minced garlic, salt, pepper, and oregano until evenly coated. Spread the fries in a single layer on a baking sheet lined with parchment paper. Bake for 30-35 minutes, flipping halfway through, until golden brown and crispy. Remove from the oven, sprinkle with Parmesan cheese, and return to the oven for an additional 5 minutes.

In a medium saucepan, heat olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes. Stir in the garlic and mushrooms, cooking until the mushrooms are softened, about 5-7 minutes. Pour in the beef broth and red wine, add thyme, and bring to a simmer. Reduce heat and let simmer for about 15-20 minutes until slightly thickened. Season with salt and pepper to taste.

Preheat your grill to high heat. Season the entrecôte steaks generously with salt and pepper on both sides. In a small saucepan, melt the butter and stir in the chopped basil. Grill the steaks for about 4-5 minutes on each side for medium-rare, basting with the basil butter during the last minute of cooking. Remove the steaks from the grill and let rest for 5 minutes.

Plate the entrecôte alongside the garlic-Parmesan fries. Drizzle the velvety mushroom jus over the steak and fries. Garnish with additional fresh basil if desired. Enjoy your meal!