In a medium bowl, combine the oregano, smoked paprika, garlic powder, 1/2 teaspoon salt, and black pepper. Toss the bite-sized chicken pieces in the spice mixture until well coated.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the seasoned chicken and sear for 3–4 minutes per side until golden. Remove chicken to a plate and set aside.

Reduce heat to medium. Add the chopped onion to the same skillet and sauté for about 3 minutes until softened. Add the minced garlic and cook for another 30 seconds, stirring constantly. Return the seared chicken to the skillet and stir to combine with the onion and garlic. Remove from heat.

In a separate bowl, whisk together the eggs and Greek yogurt until smooth. Season lightly with salt and pepper.

Lightly grease a 9x9-inch baking dish with olive oil. Layer half of the sliced zucchini in the bottom. Spread half of the chicken-onion mixture over the zucchini. Pour half of the yogurt-egg mixture evenly on top. Sprinkle with half of the shredded mozzarella and half of the Parmesan. Repeat with the remaining zucchini, chicken mixture, yogurt-egg mix, and finish with the remaining cheeses.

Cover the dish loosely with foil and bake at 375°F for 20 minutes. Remove the foil and bake an additional 10–15 minutes, until the cheese is melted, bubbly, and lightly golden. Let the bake rest for 5 minutes before slicing and garnish with chopped fresh parsley or basil, if desired.