Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

Cut the vegetables (such as zucchini, eggplant, or mushrooms) into slices or small pieces.

In a bowl, mix breadcrumbs, grated Parmesan cheese, salt, and pepper.

Dip the vegetable pieces into beaten egg and then coat them with the breadcrumb mixture.

Place the breaded vegetables on the baking sheet and bake for 20-25 minutes, or until golden and crispy.

Meanwhile, warm the sandwich rolls in the oven or on a grill pan.

Assemble the sandwich by placing a layer of lettuce on the bottom half of each roll.

Add the baked vegetable patties on top of the lettuce.

Drizzle with your favorite sauce (such as barbecue or mayonnaise).

Top with the other half of the roll and serve immediately.