In the same braiser over medium-high, combine the remaining 1 tablespoon oil, reserved grated onion, remaining garlic, ½ teaspoon salt and ¼ teaspoon pepper.
Cook, scraping up any browned bits, until the moisture from the onion has evaporated and the onion and drippings are well browned, about 5 minutes; reduce the heat as needed if browning goes too quickly.
Stir in the tomato paste and remaining 1 teaspoon oregano, and cook for a minute or two.
Add the grated tomatoes and scrape up any browned bits.
Bring to a simmer over medium-high and cook, stirring often, until the mixture is slightly thickened, 4 to 5 minutes.