Preheat oven to 375° F.
In a large bowl, mix ground venison, 1 tablespoon olive oil, grated Pecorino Romano cheese, and seasonings until well combined.
Heat a skillet over low heat with 1 tablespoon olive oil. Sauté the spinach until wilted, about 1–2 minutes, then remove from heat.
Lay a long piece of plastic wrap on a cutting board and place the ground meat in the center. Press the meat to about ½-inch thickness. Layer the prosciutto, provolone cheese slices, and wilted spinach on top.
Using the plastic wrap, roll the meat tightly from the longest side, keeping pressure to secure the stuffing inside. Place the rollup on a baking pan and remove the plastic wrap.
Drizzle the rollup with the remaining olive oil and loosely cover with foil.
Bake for 35–40 minutes, or until the internal temperature reaches 130-135°F or until your preferred doneness.
Remove from the oven and let rest for 10 minutes. Slice and serve.