Cut off asparagus tips and set aside (they will be blanched and used as a garnish). Chop remaining spears into 1/2-inch pieces.
In a small skillet or saucepan, bring 1/2 cup water to boil. Add asparagus tips, cover, and cook until tender, about 2 minutes. Remove from the pan and set aside to cool.
In a large saucepan over medium heat, melt butter. Stir in chopped asparagus spears and leeks and cook until softened, about 8 to 10 minutes.
Add broth and bring to a simmer. Cook until vegetables are completely tender, about 5 minutes. Stir in peas and Parmesan.
Working in batches, transfer to a blender and process soup until smooth, about 2 to 3 minutes. Wash out saucepan, then add back blended soup.
Over medium-low heat, stir in half-and-half and lemon juice. Season to taste with salt (I like 3/4 teaspoon). Garnish with reserved asparagus tips.
Asparagus: Look for stalks that are firm, straight, and smooth, with tips that are fresh-looking and have closed buds. Asparagus should be a vibrant green with a slight violet hue at the tips and ends. If the asparagus is not being stored in a shallow pan of water, ice, or on a damp pad, check the ends to see if they’re not completely dried out or flaky. Avoid asparagus that looks wilted, wrinkled, or has darkened black tips that are falling off the stalk. These are all signs the asparagus is past its prime. You'll want stalks of uniform size so they cook evenly. Trim off the thicker ends to give each stalk a fresh cut, then use a vegetable peeler or paring knife to shave down thicker stalks so they're about the same size as any thinner ones.
Chicken broth: Store-bought or homemade Chicken Broth; choose your favorite. For a vegetarian Cream of Asparagus Soup, swap in vegetable broth.
Parmesan cheese: Or Pecorino. Just make sure that you use fresh Parmesan or Pecorino, shredded from a block, rather than the Parmesan that comes in the green can. (Although that has its place, too!)
Half-and-half: This is my preferred dairy for this recipe. If you like, substitute sour cream or plain Greek yogurt.
Yield: This Cream of Asparagus Soup makes about 6 cups of soup, enough for 6 (1-cup) servings (or 3 larger, 2-cup servings).
Storage: Store leftovers covered in the refrigerator for up to 4 days.
Make ahead: The soup can be made up to 3 days in advance and reheated on the stove.
Freezing: Cream of Asparagus Soup is great for the freezer, and putting a batch on ice is a lovely way to savor some spring flavor after the season passes. Cool soup completely, then divide into freezer-safe containers (I love pint-sized glass mason jars). Leave 1/2-inch head space for expansion, then date, label, and freeze for up to 3 months. Thaw overnight in the refrigerator.