Preheat oven to 400 degrees Heat olive oil in a medium-size sauté pan over medium-high heat. Add potatoes, season with salt and pepper and cook for 3-5 minutes. Add mushrooms and zucchini and continue cooking for 2-3 minutes or until vegetables begin to soften.
In a separate bowl, whisk eggs and half and half. Season with kosher salt and pepper.
Reduce heat to medium and spread the vegetable mixture evenly on the bottom of the sauté pan. Pour egg mixture over the veggies and allow eggs to cook about a minute until it starts to set Do not stir!
Sprinkle in smoked trout, oregano, goat cheese, and red onion on top of eggs and top with grated parmesan cheese.
Place pan in the oven and bake until the eggs are fully cooked and the top is golden brown, about 15 minutes.