Preheat the oven to 400 degrees F. Cut a piece of parchment paper to fit a baking sheet (or use a pre-cut sheet).
Place the puff pastry on top the parchment paper and use a rolling pin to gently thin it out to a larger rectangle. (Note: you can aim for 10x14 inches, but just make sure it’s long enough to fit the trimmed asparagus. It doesn’t need to be an exact size). Carefully place the parchment sheet onto the baking sheet.
If necessary, trim the asparagus a bit more. You want to leave space for approximately 1 inch of crust around the border which will puff up in the oven. Line the asparagus closely together over the dough.
Brush the asparagus lightly with melted butter. (Note: I had brown butter on hand, but regular unsalted butter is fine).
Crack the eggs into ramekins and slowly top over the asparagus. You can skip this step if you want. Try to keep the eggs away from the edges, but it’s fine if they side onto the crust a bit; mine did. You can also gently nudge the yolks over to evenly disperse them and make room for more.
Top generously with salt and pepper.
Bake for 20 minutes, or until the outer edges of the crust are golden brown and the whites have just set. You can either shoot for a firm or runny yolk based on preference. If you want a runny yolk, you might want to try adding the eggs midway through the cooking process.