When making soups and sauces, season with salt and pepper gradually throughout the process to layer flavors.
Melt butter in large sauce pot over medium heat. Add onion and parsnip. Sweat for 1 minute until translucent, but no color. Add asparagus. Add chicken broth and cook until vegetables are fork tender. Add tarragon, parsley, and frozen peas. Puree in blender or preferably with emersion blender. When completely pureed, add cream and bring back to a simmer.
For parmesan crisp, take cookie sheet lined with parchment paper and sprinkle parmesan in silver dollar sized circles. Bake at 325 degrees for 5-10 minutes until golden brown.
Serve asparagus soup immediately with grated lemon zest and parmesan crisp.