Wash the zucchinis and grate them using the box grater.

Place the shredded zucchini in a cheesecloth or clean kitchen towel, sprinkle with 1 teaspoon of salt, and let it sit for 10 minutes to draw out moisture.

Squeeze the zucchini firmly to remove as much liquid as possible. This step is crucial for crispy hash browns.

In a mixing bowl, combine the squeezed zucchini, egg, flour, Parmesan cheese (if using), minced garlic, onion powder, and black pepper. Mix well until a batter forms.

Heat 2 tablespoons of olive oil or butter in a large frying pan over medium heat.

Scoop about 2 tablespoons of the mixture for each hash brown and flatten it slightly in the pan with the back of a spoon.

Cook for 3-4 minutes on each side, or until golden brown and crispy. Remove from the pan and set on a plate lined with paper towels to absorb excess oil.

In the same pan, add a bit more oil or butter if needed. Crack the eggs into the pan and cook to your preferred doneness (sunny-side up, over-easy, or fully cooked). Sprinkle with salt and pepper.

Place the zucchini hash browns on a serving plate, top each with a fried egg, and garnish with optional toppings like fresh parsley or avocado slices. Serve immediately.