Grilled Eggplant and Mozzarella Panini

Name: Grilled Eggplant and Mozzarella Panini
Ingredients: 1 ½ cups firmly packed fresh basil leaves; 2 cloves garlic, sliced; ¼ cup pine nuts, toasted*; ½ cup extra-virgin olive oil; 6 tablespoons freshly grated Parmigiano-Reggiano, or pecorino cheese, or a mix; Kosher or sea salt; 2 small eggplants, about ½ pound each; 2 tablespoons extra-virgin olive oil; 4 pieces thick focaccia, halved horizontally, or 8 pieces thin focaccia, each roughly 3-by-6 inches or equivalent; 8-12 thin tomato slices; 6 ounces fresh whole-milk mozzarella cheese, thinly sliced