Preheat oven to 400 degrees F (200 degrees C). Grease 6 muffin cups.
Bring the quinoa and water to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the quinoa is tender and the water has been absorbed, 15 to 20 minutes.
Combine cooked quinoa, eggs, egg whites, zucchini, Swiss cheese, ham, parsley, Parmesan cheese, and white pepper in a large bowl and mix until thoroughly combined. Spoon mixture to the top of each prepared muffin cup.
Bake in preheated oven until the edges of frittatas are golden brown, about 30 minutes. Allow to cool at least 5 minutes in the pan before serving. Serve hot or cold.