This vegetable omelet can be served warm or cold.
Preheat oven to 325 degrees with rack in upper third. Brush a rimmed baking sheet with oil. Line with parchment; brush parchment. Whisk eggs in a bowl until combined, then slowly whisk in flour, thyme, and salt until smooth. Pour into prepared baking sheet. Sprinkle with red onion and tuck in greens.
Bake until puffed and golden, about 20 minutes. Serve warm or room temperature, cut into squares.