Cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente; drain and transfer to a large bowl.
Meanwhile, process onion, celery, carrot, and garlic in a food processor until finely chopped.
Heat oil in a large skillet over high. Add chopped vegetables, beef, and pork and cook, breaking up with a spatula, until meat is beginning to brown, about 3 minutes. Stir in tomato paste, oregano, 3/4 tsp. salt, and 1/2 teaspoon pepper; cook, stirring occasionally, until heated through, about 1 minute. Add wine and cook, stirring constantly, until reduced by half, about 1 minute more. Stir in tomato sauce, reduce heat to medium, and simmer until sauce is slightly thickened, about 4 minutes.
Remove from heat, then stir in butter. Toss meat sauce with pasta, top with Parmesan, and season with pepper.