4 scallions, thinly sliced, white and green parts separated
1 jalapeno pepper, seeded and minced
3 tablespoons chopped fresh parsley
1/4 teaspoon freshly grated nutmeg
Freshly ground pepper
1 tablespoon unsalted butter
6 large eggs
1/2 cup grated pepper jack or sharp white cheddar cheese
Use a box grater with large holes to grate the squash into a colander (or use a food processor fitted with the shredding attachment). Add 1 tablespoon of salt, toss, and allow it to drain for 30 to 40 minutes in the sink. Squash should be squeezed to extract as much liquid as you can.
Set the oven to 375 degrees Fahrenheit. In a sizable oven-safe skillet, heat the olive oil over medium-high heat. 3 tablespoons of scallion greens should be saved. Add the jalapeno, salt to taste, and the remaining scallions (white and green sections), and simmer for about 3 minutes, or until the scallions are tender. Add the shredded squash and simmer for 7 minutes, stirring periodically, until fork-tender. Add pepper, nutmeg, and parsley to taste. About 1 more minute of cooking is needed to gently dry up the mixture. After 5 minutes, turn off the heat and allow it to cool.
Squash is equally distributed in the skillet. Using the back of a spoon, make six indentations in the mixture that are 2 1/2 inches across. Fill each one with 1/2 teaspoon of butter. Each egg should be cracked into a small bowl one at a time, then placed into an indentation. Add the cheese and season with salt and pepper.
Place the skillet in the oven, and bake for 10 to 12 minutes, or until the egg whites are set and the yolks are cooked to your preference. Add the scallion greens you set aside on top.