1/2 to 3/4 pound asparagus
Olive oil, as needed
Salt, to taste
1/4 cup fresh breadcrumbs
A few leaves fresh thyme
Freshly ground black pepper, to taste
1 tablespoon red-wine or sherry vinegar
Prepare the asparagus: If it is thin, simply cut off bases. If stalks are thicker than a No. 2 pencil, cut off bases and peel, starting at tips with light pressure and gradually increasing pressure as you work your way down stalks until you're pressing quite firmly near ends.
In a tightly sealed pot over rapidly boiling water, steam asparagus until just tender, 2 to 3 minutes for thin asparagus, 4 to 5 minutes for thick. Drain, pat dry, dress lightly with 1 tablespoon oil, season with a pinch of salt and keep warm.
Place the breadcrumbs in a bowl. Season lightly with the salt and thyme leaves and add enough oil to generously coat, about 1 tablespoon.
Transfer breadcrumbs to a small nonstick skillet and place over medium heat. Cook, stirring occasionally, until they begin to darken. When they have fried enough that they feel dry when you stir them and make a dry, static-y sound, 2 to 3 minutes, divide them into 2 equal batches and pat to make a thin layer.
Crack the eggs over breadcrumbs. Season with salt and freshly ground pepper, cover tightly and cook eggs until they're as done as you like (they are best with yolks left runny; if you prefer over-easy, you can flip them).
Divide asparagus in half and arrange it on 2 warm plates. When eggs are done, drape 1 egg over each asparagus bundle. Add the vinegar to empty pan and let it sizzle for a moment before drizzling it over eggs. Serve immediately.
Makes 2 servings.