Preheat the oven to 350 degrees F. Heat the oil in a 10-inch ovenproof skillet. Add the asparagus and cook over medium-low heat until softened but not browned, about 6 minutes.
Meanwhile, in a medium bowl, beat the eggs, greens, milk, cheese if using and 1/4 teaspoon each salt and pepper.
Add to the skillet with the asparagus; cook until the eggs begin to set at the edges, about 30 seconds. Using a spatula, lift the edges and tilt the pan, letting the uncooked eggs seep underneath. Cook until the bottom is set, about 3 minutes. Transfer to the oven and bake until fluffy, 6 to 8 minutes; cut into 6 wedges.
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