Preheat the oven to 400°F (200°C). Bring a large pot of salted water to a boil for the tortellini.
Heat a 12-inch oven-safe skillet over medium heat. Add the ground beef or turkey and cook, breaking into small pieces, until browned.
Season the browned meat with kosher salt, black pepper, dried basil, and dried oregano. If the meat is very lean, add a drizzle of olive oil as needed.
Stir the marinara sauce into the skillet with the meat and reduce the heat to low to keep it warm while you cook the tortellini.
Cook the cheese tortellini in the boiling salted water according to package directions (about 3–4 minutes), then drain in a colander.
Add the drained tortellini to the meat and sauce, gently folding with a spatula to combine without breaking the pasta.
Distribute the torn fresh mozzarella evenly over the top of the tortellini and sauce.
Transfer the skillet to the preheated oven and bake for 20–25 minutes, until the cheese is melted, golden, and bubbly.
Remove from the oven and sprinkle with grated Parmesan and fresh basil before serving.