Peel asparagus and cut off the woody ends. Rinse asparagus. Bring water to a boil and add asparagus peelings and ends. Cover and cook for 15 minutes.
Trim the crusts from the bread. Cut into small squares. Melt butter in a pan and sauté until the bread is golden on both sides. Remove from heat and set aside.
Pour asparagus cooking water through a sieve into another pot, squeeze out solids and discard. Cut the asparagus into 2 cm (approximately 3/4-inch) long pieces.
Bring the asparagus broth to a boil. Add asparagus spears and cook for 10 minutes on low heat. Whisk egg yolks with the cream and a little broth and stir into the hot (not boiling) soup. Season with salt and pepper. Distribute soup on plates and sprinkle with chervil leaves and croutons.