Line a baking sheet with a large piece of parchment paper creased down into the corners and allow it to overlap the sides of the baking sheet, set aside.
In a large bowl whisk the eggs, kosher salt, pepper, and Parmesan.
Grate the zucchini on the large holes of a box grater.
Wrap the zucchini in a towel and squeeze out as much liquid as you can out of the zucchini.
Whisk the zucchini shreds in with the eggs.
Pour the egg mixture into the prepared baking sheet and spread in a thin even layer covering the bottom of the sheet. Place in the oven for 20 minutes or until the eggs are set and solid through out.
Remove from the oven and turn the oven off. Sprinkle the egg with the cheddar cheese.
Carefully roll the egg over the cheese, peeling away the parchment paper as you go. Brush the roll with butter and sprinkle with chives then loosely cover with the parchment paper and place in the OFF oven. Allow the roll to sit in the oven until the cheese melts about 5-10 minutes.
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