Grate the zucchini using the large holes of a box grater or a food processor with a grating attachment. Place the grated zucchini in a colander, sprinkle with 1 teaspoon of salt, and toss to combine.
Let the zucchini sit for at least 30 minutes to draw out excess moisture.
After 30 minutes, use your hands to squeeze out as much liquid as possible from the zucchini. Transfer the squeezed zucchini to a clean kitchen towel and give it one final, vigorous squeeze.
In a large mixing bowl, combine the drained zucchini with flour, Parmesan cheese, garlic, onion, egg, oregano, black pepper, and paprika. Mix thoroughly until all ingredients are evenly incorporated.
Using a 1/4 cup measuring cup, scoop the mixture and shape into patties approximately 3 inches in diameter and 1/2 inch thick. Slightly flatten each patty with your palm for even cooking.
Heat olive oil in a large skillet over medium heat until shimmering. Working in batches to avoid overcrowding, carefully place the patties in the hot oil.
Cook for 3-4 minutes per side until golden brown and crispy. For maximum crispiness, resist the urge to flip them prematurely.
Transfer to a paper towel-lined plate to absorb excess oil. Serve warm.