Make the marinara sauce: Heat the olive oil in a medium saucepan over medium-high heat. Add the sliced garlic and cook, stirring, until lightly golden, 2 to 3 minutes. Stir in the oregano, then add the tomatoes, 1/2 teaspoon salt and a few grinds of pepper. Bring to a boil, then reduce the heat to a gentle simmer and cook, stirring occasionally, until thickened, 12 to 15 minutes. Season with salt and pepper. Cover and set aside until ready to serve. (For a smoother sauce, puree with an immersion blender.)
Meanwhile, make the meatballs: Combine the beef, sausage, shredded mozzarella, parmesan, breadcrumbs, parsley, grated garlic, milk, egg, 1 teaspoon salt and a few grinds of pepper in a large bowl; mix with your hands until combined. Form into 1 1/2-inch meatballs (about 24).
Make the kebabs: Preheat a grill to medium high. Combine the eggplants, broccoli, olive oil, 1 teaspoon salt and a few grinds of pepper in a large bowl; toss to coat. Thread the meatballs, eggplant and broccoli onto eight 12-inch skewers.
Brush the grill grates with olive oil. Grill the kebabs, covered and turning occasionally, until the meatballs are cooked through and marked and the vegetables are charred around the edges, about 15 minutes; drape a slice of mozzarella over each meatball during the last minute of cooking. Remove to a platter. Reheat the marinara sauce if needed. Serve the kebabs in rolls with the marinara sauce, parmesan and red pepper flakes.
If you use wooden skewers, soak them in water for at least 30 minutes so they won't burn.