Preheat broiler.

Trim away the ends of the zucchini, and then cut lengthwise. Toss with 1 tablespoon of extra-virgin olive oil and season with salt and pepper. Arrange on baking sheet, cut side up. Broil until lightly browned, then turn and broil on the skin side until the zucchini are just tender. Transfer to a cutting board and slice crosswise about 1/4-inch thick.

Stir the zucchini and basil into the beaten eggs. Season with salt and pepper.

Heat a 10-inch flameproof nonstick skillet over moderate high heat. Add the remaining 1/2 tablespoon olive oil. When skillet is hot, add the egg mixture. Let the eggs cook without stirring until they begin to set, then lift the edges with a spatula and let the uncooked eggs run underneath. Continue cooking until the eggs are mostly cooked but still a little moist on top. Place the skillet under the broiler just until the surface of the frittata no longer moist, about 30 seconds, then sprinkle the cheese on top and broil again until the cheese melts, about 30 seconds longer. Slide the frittata onto a serving plate and let cool to room temperature.

Set the oven temperature to 375 degrees F. Brush the bread slices on both sides with olive oil, season with salt and pepper, place on baking sheet. Bake until lightly browned and crisp.

Cut the frittata into slices, place on warm slice of toast, place 1/2 slice of tomato on top of frittata, season with salt and pepper and chili flakes to taste, and cover with another piece of toast. Serve.