Although most mushrooms should not be soaked, morels are the exception. They have a unique, honeycomb-like interior that traps bugs, soil, and grit, so they must be washed in several waters in order to be fully cleaned.
Prepare the mushrooms by trimming the ends and repeatedly soaking and rinsing them in salted water until the water runs clear. Set aside to drain on a clean tea towel or paper towel.
Step 2
Blanch the asparagus by adding a little water (about a ½ cup) to a skillet with the asparagus and cover. Cook for about 3 minutes, or until the asparagus is bright green but still crisp. Drain, and immediately plunge the asparagus into ice water for one minute to stop the cooking.Wrap the cooked asparagus in a dry, clean kitchen towel, and set aside.
Step 3
In a large skillet, heat the butter over medium heat until melted. Add the morels, and stir to coat. Season with salt (use a lighter or heavier hand depending on how salty your stock is), and cook morels gently for 5-6 minutes, stirring occasionally. Add the stock to the pan, and simmer gently while you cook the eggs.
Prepare four shallow serving bowls on your counter, so that they will be ready as soon as your eggs are. Divide the mushrooms, stock, and asparagus evenly between the dishes.
Step 4
To make poached eggs, boil water in a small saucepan. Crack the eggs, two at a time, into a small ramekin, and set next to your stove.Once the water is boiling, stir the water rapidly in one direction using a wooden spoon, creating a “tornado” effect.Slide the eggs, two at a time, gently into the water, and immediately turn the heat down so the water simmers. Remove the eggs with a slotted spoon after 2-3 minutes. A perfectly-poached egg has a firm white and a runny yolk, and will jiggle slightly when prodded.
Step 5
Top the asparagus with a poached egg. Finish with lemon zest and fresh chives, and serve immediately.