Prepare for baking by preheating your oven to 350°F / 175°C and lightly greasing a 3-quart (approx. 9x13 inch) rectangular baking dish.
In a large skillet, heat the olive oil over medium-high heat.
Add the eggplant, zucchini, red peppers, onion, garlic, salt, and pepper.
Sauté for 10-15 minutes, stirring occasionally, until the vegetables are tender.
While the vegetables cook, whisk together the eggs and mayonnaise in a large bowl until smooth.
Stir in 1 cup (115g / 4.1 oz) of the mozzarella cheese and all of the Pecorino-Romano cheese.
Gently fold the cooked vegetables into the cheese and egg mixture until well combined.
Pour this mixture into your prepared baking dish, spreading it evenly.
Sprinkle the remaining 1 cup (115g / 4.1 oz) of mozzarella cheese over the top, followed by the crushed crackers.
Bake uncovered for 20-25 minutes, or until the top is golden brown and a knife inserted into the center comes out clean. Allow the casserole to rest for 10 minutes before serving; this helps it set for perfect slices.
Don't have round crackers? Panko breadcrumbs mixed with a tablespoon of melted butter make an excellent crunchy topping.
Seasoned croutons or even crushed potato chips also work in a pinch.
