Toss zucchini, bell pepper, and onion with 2 tablespoons olive oil, oregano, 1/2 teaspoon salt, and pepper. Make sure every piece is lightly coated - this prevents sticking and helps with char.

Heat grill or grill pan to medium-high. Grill vegetables in batches without crowding: zucchini and peppers 3-4 minutes per side until tender with dark grill marks, onions 4-5 minutes per side until softened and charred at edges. Transfer to a cutting board as done.

Once cool enough to handle, chop vegetables into bite-sized pieces. They should be chunky enough to stay put in the wrap. Keep warm or at room temperature.

In a food processor, combine parsley, mint, garlic, lemon juice, capers, remaining 1 tablespoon olive oil, and remaining 1/2 teaspoon salt. Pulse until finely chopped, then with motor running, drizzle in 1/3 cup olive oil until sauce is loose and spoonable. Taste and adjust lemon or salt - it should be bright and salty.

Warm flatbread on the grill for 30 seconds per side or in a dry skillet until pliable. Spread 2 tablespoons herb sauce down the center, top with a handful of greens, a generous scoop of grilled vegetables, and a crumbling of feta. Drizzle with more sauce if desired.

Fold bottom edge up, then fold in sides and roll tightly away from you. Slice in half on the diagonal and serve immediately, with extra sauce on the side.