Preheat a broiler.

Trim away the ends of the zucchini, then cut in half lengthwise. Toss with 1 tablespoon of the oil and season with salt and pepper. Arrange on a 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 moderately high heat. Add the remaining 1/2 tablespoon olive oil. When the skillet is hot, add the egg mixture. Let the eggs cook without stirring until they begin to set, then lift the edges with a rubber spatula and let the uncooked egg 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 is 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.

Reset the oven temperature to 375ºF. Brush the bread slices on both sides with olive oil, season with salt and pepper, and place on a baking sheet. Bake until browned and crisp, about 15 minutes.

Cut the frittata into wedges to serve. Accompany each serving with 2 warm slices of toast.