Preheat oven to 350°. In a Dutch oven, heat 1 tablespoon oil over medium-high heat.
Add half of the zucchini, half of the onions and 1/2 teaspoon oregano; cook and stir 8-10 minutes or until zucchini is crisp-tender. Remove from pan. Repeat with remaining vegetables.
Return previously cooked vegetables to pan. Stir in salt and pepper. Cool slightly.
In a large bowl, whisk eggs and baking powder until blended; whisk in yogurt and flour just until blended. Stir in cheese, parsley and zucchini mixture.
Transfer to a greased 13x9-in. baking dish. Sprinkle with paprika.
Bake, uncovered, 30-35 minutes or until golden brown and set. Let stand 10 minutes before cutting.