1 to 1 1/2pounds asparagus, trimmed and peeled Salt and black pepper to taste
6 tablespoons (3/4 stick) butter, or more
4 eggs
8 thin slices ham, optional
12 or 16 paper-thin slices Parmesan cheese
Instructions
Poach or steam the asparagus in or over boiling salted water until it is bright green and just tender, 3 to 7 minutes, depending on its thickness. Meanwhile, put 4 tablespoons of the butter in a small saucepan and turn the heat to low.
Add at least 2 tablespoons butter to a large skillet, preferably nonstick, and turn the heat to medium. When the butter melts, crack the eggs into the skillet and cook, sprinkling with salt and pepper and adjusting the heat as necessary, until the whites are no longer runny, about 5 minutes.
Drain the asparagus when it is done and divide among 4 plates. Turn off the heat under the butter the moment it begins to turn brown; if the eggs are not quite ready, keep it warm over the lowest possible heat.
Top the asparagus with a portion of ham if you’re using it, then a fried egg, then a drizzle of the browned butter, and finally a few slices of Parmesan. Serve immediately.