Make the pasta sheets. Sprinkle with semolina flour or cornmeal. Keep on a large baking sheet covered with a lightly damp kitchen towel.
Melt the butter in a large saucepan over medium heat. Add the onion, celery, and carrots and sauté until soft, about 5 to 7 minutes.
Add the beef and break it up with a wooden spatula or spoon. Cook until no longer pink. Safely discard of most of any rendered grease, leaving about 1 tbsp in the pan. Season the meat with salt, pepper, and Italian seasoning.
Stir in the red wine and simmer until almost all the liquid has evaporated. Remove from heat and let cool slightly (at least 15 minutes).
Carefully transfer the meat mixture to a food processor. Add the eggs, cheese, and breadcrumbs. Purée until smooth. Transfer to a bowl and set aside.
Lay a pasta sheet on a lightly floured surface. Fold the sheet over, lengthwise, halfway, and then open it back up. This will help you keep an eye on where the center of the sheet of pasta is. Each pasta sheet should be about 4 inches wide.
Beginning about 1 inch from one of the short ends, place teaspoons of the filling about 1 inch apart in a straight row down the center of one side of the fold. Dip a pastry brush in water (or your fingertip) and lightly brush water around each mound of the filling.
Fold the dough over the filling, molding it around the filling to press out any air pockets. Use your fingertips and firmly press the edges of the dough together to seal.
Use a fluted pastry wheel (or a sharp knife) to cut between the mounds of filling. Separate the squares and place, without touching, in a single layer on a floured baking sheet. Cover with a lightly damp kitchen towel. You can cook them immediately, or, keep them covered for up to 2 hours.
Bring a pot of liberally salted water to a boil.
Heat the oil in a saucepan over medium heat. Add the minced garlic and sauté for several minutes. Add the tomatoes and cook, stirring often, and pressing on the tomatoes occasionally, for about 7 minutes.
Season with salt, pepper, and fresh basil.
Carefully place the prepared ravioli into the boiling water. Cook for about 3 to 4 minutes. Carefully drain.
Divide the ravioli among plates, top with the sauce and additional freshly grated parmesan and chopped fresh basil.
