Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil and place a cooling rack on top.

Combine ground venison, Italian sausage, Parmesan cheese, bread crumbs, egg, white wine, garlic, basil, and oregano in a large bowl; stir until well combined. Scoop meat mixture from the bowl and form into 2-inch balls. Place meatballs on top of the cooling rack.

Bake in the preheated oven until meatballs are cooked through, about 25 minutes. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C).

As soon as meatballs go in the oven, begin the sauce: heat olive oil and butter in a large skillet over medium-high heat. Add mushrooms and thyme; cook until mushrooms are dark brown in color, about 10 minutes.

Whisk together half-and-half, mustard, and cornstarch in a small bowl. Pour half-and-half mixture over mushrooms, reduce heat, simmer for 5 minutes, stirring continually. Turn heat off, season with salt and pepper, and let sit to thicken.

Remove meatballs from the oven, transfer to a serving plate, and drizzle with mustard sauce.