Grate the zucchini into a colander in the sink. Add 1½ teaspoons salt and toss with the zucchini. Let the colander sit in the sink while the salt helps to draw the moisture out of the zucchini for about 10 minutes. Then squeeze out any extra moisture.
Place a paper towel in large mixing bowl. Place the zucchini on top and allow it to sit for several minutes to absorb more moisture. After a few minutes, remove the paper towel and leave the zucchini in the bowl. Add the shallots, dill, eggs, cheese, flour, and oregano. Gently mix all of the ingredients together.
Heat about 1 tablespoon of coconut oil in a large skillet over medium heat. Drop the batter in 1 teaspoon mounds into the heated oil. Only put a few in the pan at a time so that they don’t become crowded. Flatten each mound with a spatula and cook for 3-4 minutes on each side, until golden brown. Drain on paper towels and sprinkle with salt to taste. Repeat until you have used up all of the batter, adding additional oil to the pan as needed.
Serve immediately or keep in the refrigerator. When ready to serve, simply place on a baking sheet and reheat in a 325ºF oven until warm and crisp again.
Notes
Note: If desired, you can serve the fritters with a quick, creamy dipping sauce. Mix 1 cup plain Greek yogurt with 2 tablespoons fresh chopped dill, 1 tablespoon lemon juice, and salt to taste. Serve alongside the fritters.