Hold the untrimmed end of the asparagus and using a vegetable peeler, shave the asparagus (video here). Heat a 12" skillet over medium-low heat. Add the olive and coat the bottom of the pan. Place the asparagus in the pan along with the pesto and toss until the asparagus is well coated.

Cook the asparagus for about 1 minute then create four spaces for the eggs. Crack an egg into each space. Cook until the whites are set and the yolks are to your desired firmness; 10 to 15 minutes. If the whites are not firming up, cover the pan. Or heat a small amount of oil in a separate pan and spoon over the egg whites.

Before serving, sprinkle with the bread crumbs,  grated parmesan, and/or chili flakes.