Heat 2 teaspoons oil in a 10-inch nonstick skillet over medium heat.
Add zucchini and onion; cook, stirring often, for 1 minute.
Cover and reduce heat to medium low; cook, stirring occasionally, until the zucchini is tender, but not mushy, 3 to 5 minutes.
Add tomatoes, mint, basil, ⅛ teaspoon salt and a grinding of pepper; increase heat to medium high and cook, stirring, until the moisture has evaporated, 30 to 60 seconds.
Whisk eggs, the remaining ⅛ teaspoon salt and a grinding of pepper in a large bowl until blended.
Add the zucchini mixture and cheese; stir to combine.
Preheat the broiler.
Wipe out the pan and brush it with the remaining 2 teaspoons oil; place over medium low heat.
Add the frittata mixture and cook, without stirring, until the bottom is light golden, 2 to 4 minutes. As it cooks, lift the edges and tilt the pan so uncooked egg will flow to the edges.
Place the skillet under the broiler and broil until the frittata is set and the top is golden, 1½ to 2½ minutes.
Loosen the edges and slide onto a plate. Cut into wedges and serve.