Mozzarella di Bufala with Shell Beans

Name: Mozzarella di Bufala with Shell Beans
Ingredients: 1 cup finely chopped onion; 6 large garlic cloves, smashed; 4 fresh sage leaves; 1 cup fresh shell beans (such as cranberry, cannellini, flageolet, or lima; about 6 ounces) or ¾ cup dried; 2 cups (packed) whole fresh basil leaves, divided; ½ cup extra-virgin olive oil, divided; 1 tablespoon pine nuts, toasted; 1 large garlic clove, smashed; ½ teaspoon kosher salt plus more for seasoning; Freshly ground black pepper; 8 ounces assorted fresh beans (such as green beans, yellow wax beans, Italian flat beans, or haricots verts); Kosher salt; 3 scallions, thinly sliced on the diagonal (about 1 cup); 1 tablespoon plus 1 teaspoon fresh lemon juice; 4 3-ounce balls buffalo mozzarella, halved diagonally, or one 12-ounce ball cut into 8 equal pieces; ½ cup Slow-Roasted Cherry Tomatoes; optional (click for recipe)