Grilled Eggplant, Broccoli Rabe, And Mozzarella Sandwich

Ingredients

• 2 italian eggplants, ends trimmed, sliced 1/4-inch thick lengthwise
• 5 tablespoons olive oil, divided
• kosher salt and freshly ground black pepper
• 2 medium garlic cloves, thinly sliced
• 1/4 teaspoon red pepper flakes
• 1 bunch broccoli rabe, hard ends trimmed, cut into 2-inch pieces
• 1/2 cup homemade or store-bought low-sodium chicken or vegetable broth
• 4 ciabatta-style rolls, halved horizontally
• 1 (1 pound) ball fresh mozzarella, sliced into 1/4-inch disks
• fresh basil leaves, chopped