Skillet Eggs With Squash (2/3)

Ingredients:
(6 servings)

3 pounds (6 medium) summer squash and/or zucchini
Kosher salt
2 tablespoons extra-virgin olive oil
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