Drain mozzarella on paper towels for 15 minutes and blot the cubes dry. Process with ricotta, 1 tablespoon olive oil, 1/4 teaspoon salt and pepper until a thick spread forms, stopping to scrape the bowl.

Heat remaining oil in a skillet over medium-high heat. Add whole cherry tomatoes and cook for 6 to 8 minutes, shaking the pan, until blistered and softened with a few beginning to split.

Remove the pan from heat and let tomatoes cool for 5 minutes. Lift them into a bowl, leaving loose juices behind, and fold with basil, balsamic and remaining salt.

Split the rolls and toast their cut faces under the broiler for 1 to 2 minutes. Let cool briefly, then spread the mozzarella mixture generously along both cut faces.

Divide warm tomatoes among rolls and close gently without flattening the cheese spread. Cut across the middle; serve one sub per person.