1 1/4 pounds ripe medium tomatoes, cored and halved crosswise
2/3 cup freshly grated Pecorino Romano cheese (about 2 1/2 ounces)
2 scallions, cut into 2-inch pieces
1 jalapeño, seeded and coarsely chopped
1 tablespoon tomato paste
1 1/2 teaspoons whole marjoram leaves
1/4 cup extra-virgin olive oil
Salt and freshly ground pepper
Working over a strainer set over a bowl, remove the tomato seeds. Using a wooden spoon, press down on the seeds to extract as much juice as possible. Discard the seeds and reserve 1/4 cup of the juice. Cut the tomatoes into chunks.
In a food processor, combine one-quarter of the tomatoes with the tomato juice, cheese, scallions, jalapeño, tomato paste and marjoram. Add the remaining tomatoes and pulse until coarsely chopped; the sauce should be chunky. Transfer the sauce to a bowl, stir in the oil and season with salt and pepper.
Grilled shrimp, chicken breasts, vegetables or peasant bread.