- 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 pan 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.