Position a rack in the upper third of the oven and preheat to 450 degrees F. Whisk the whole eggs and whites in a bowl. Add the cottage cheese and whisk until almost smooth. Whisk in the gouda and rosemary.
Cook the garlic in the olive oil in a 10-inch nonstick ovenproof skillet over medium-high heat until it starts to brown, 1 to 2 minutes. Add the onion, season with salt and cook 2 minutes. Add the vegetables, increase the heat to high and cook until just tender, about 5 minutes.
Reduce the heat to medium. Spread the egg mixture evenly in the pan. Cook, undisturbed, until a thin crust forms on the bottom, about 2 minutes. Run a rubber spatula around the edge to release the egg from the pan. Continue cooking until the bottom is golden, 2 to 3 more minutes. Sprinkle with the parmesan and paprika; transfer to the oven and bake until just set, 5 to 7 minutes. Remove from the oven, cover and let sit, 5 to 7 minutes. Cut into wedges and serve with the bread.