Trim the zucchini and coarsely grate them on a box grater. Put the grated zucchini in a colander and squeeze out as much liquid as possible with your hands.

In a medium bowl, combine the zucchini, onion, flour, fennel, dill, baking powder, oregano, nutmeg, 1/2 teaspoon salt, and 1/8 teaspoon pepper and mix well. The mixture should be just moist enough to form into patties. For each fritter, press 2 generous tablespoons of the mixture into a patty about 3 inches in diameter and 1/4 inch thick. Arrange them in a single layer on a cookie sheet.

Pour the oil into a 12-inch skillet to a depth of 1/4 inch. Heat the oil over medium-high heat until it begins to ripple and bubbles immediately when the edge of one patty is dipped into it. Using 2 slotted metal spatulas (one to lift a patty and the other to push it off the spatula), add as many patties as will fit in the pan without crowding and fry, flipping once, until golden brown and crisp on both sides, 1 to 3 minutes per side. Transfer the fritters to a paper-towel-lined plate and repeat with another batch, adding more oil as needed.

Arrange the fritters on a platter and sprinkle with both cheeses. Serve warm.

The fritters can be made and shaped several hours ahead; fry them close to serving. Keep warm in a 200 degrees F oven until ready to serve.