When the vegetables are soft, add the garlic and stir for a few minutes until fragrant. Raise the flame under the pan to high heat and add the ground meats, breaking them up with a spoon as you incorporate them. Sprinkle lightly with salt and pepper. Cook, stirring frequently, until the juices have released and the meat begins to caramelize, about 12 minutes. You should hear a popping sound rather than a sizzle coming from the pot.
Pour the wine into the pot and scrape the bottom of the pan releasing the brown bits that have formed on the bottom. Cook until the wine has reduced. Pour the tomatoes into a bowl and crush them with your hands or a potato masher into small pieces, and then stir into the pot to combine. Bring the sauce to a simmer and cook over low heat until the meat is tender and the sauce has thickened, about 1 hour. If it reduces too much and becomes dry while cooking, add water as needed 1/4 cup at a time. Taste and add salt and pepper as needed.
Bring an 8- to 12-quart pot of water to a boil. When boiling, add 2 tablespoons salt. Add the tortelli and cook according to the package instructions. Serve the ragu over the pasta with grated Parmigiano.