Set one of the oven racks about 4 inches from the broiler and preheat the oven to 375°F.
Bring a large pot of salted water to a boil. Add the ravioli and cook according to the package directions just until al dente. Drain the ravioli and set aside.
In a large cast-iron skillet or sauté pan set over medium-high heat, cook the sausage, breaking it apart with a spatula, until cooked through and no longer pink. Add the garlic and cook, stirring, for 2 minutes. Add the crushed tomatoes, tomato sauce, oregano, sugar, salt, and pepper. Cook for 5 minutes, then taste and season the sauce with additional salt and pepper.
Add the ravioli to the skillet and toss to combine. Stir in half of the shredded mozzarella cheese, then sprinkle the remaining mozzarella cheese on top. Bake for 10 minutes. Turn on the broiler, transfer the skillet to the oven rack directly under the broiler, and broil until the cheese begins to bubble and brown, about 2 minutes.
Remove the skillet from the oven and serve.
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