Begin by grating the zucchini by hand or in a food processor. It’s best to use small zucchini, as they contain less water.
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Once grated, place the zucchini on several layers of paper towels and squeeze out as much water as possible. Depending on how much water is in the zucchini, you may need to repeat this step.
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Next, melt a few tablespoons of butter in a 10-inch cast iron or oven-proof nonstick pan.
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Add the shallots, zucchini, and 1/2 teaspoon salt.
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Cook for 7 to 8 minutes, until the zucchini is tender and cooked down.
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Meanwhile, combine the eggs, remaining salt, pepper and heavy cream in a large bowl.
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Whisk to combine.
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Add the cooked zucchini and grated cheese to the egg mixture and stir.
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Pour the frittata mixture back into the pan.
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Bake for about 25 to 30 minutes, or until just set.