In a small bowl, whisk together oil and vinegar. Season with salt and pepper.
Halve each loaf, starting at one side, but don't cut through second side. Press loaves open and remove some soft center to hollow out slightly. Brush each loaf generously with oil mixture; set aside some oil mixture.
Cover each bottom half with salami and then tomatoes; brush tomatoes with remaining oil. Insert basil leaves between tomato slices. Close sandwiches and wrap each with 2 layers of plastic wrap or aluminum foil; place on a baking sheet and put in refrigerator. Place a large cutting board or another baking sheet on sandwiches and weigh it down with about 12 pounds of canned food to press sandwiches; refrigerate for 3 hours (see inset above). Quarter crosswise and serve.