Set the oven to 350 degrees Fahrenheit. In a 10-inch oven-safe skillet, heat the oil. Over medium-low heat, add the asparagus and simmer for about 6 minutes, or until tender but not browned.
In the meantime, whisk the eggs, greens, milk, and cheese, if using, and 1/4 teaspoon each of salt and pepper in a medium bowl.
Add to the skillet along with the asparagus and heat for 30 seconds or until the edges of the eggs start to set. Lift the edges of the pan with a spatula and tilt it to allow the raw eggs to seep underneath. Cook for about 3 minutes, or until the bottom is set. Transfer to the oven and bake for 6 to 8 minutes, or until fluffy; then cut into 6 wedges.
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