Preheat oven to 350 degrees F (175 degrees C). Grease a 9x9 inch baking pan.
Whisk eggs in a large bowl until smooth. Stir in cream corn, Parmesan cheese, oil, sugar, garlic, and pepper. Fold in onions, squash, and biscuit mix. Pour into prepared baking pan.
Bake in preheated oven until bubbly and lightly browned, 30 to 40 minutes.