Cut 1-2 inch of the stem end and reserve, these are the tough parts that are not pleasant to eat.

Cut 1-2 inch tips from asparagus and reserve, these are the tender chunks for garnish at the end.

Cut remaining tender stalks into 1/2-inch pieces.

Cook onion in 2 tablespoons butter in a 4-quart heavy pot over moderately low heat, stirring, until softened.

Add tender asparagus stalk pieces and salt and pepper to taste, then cook, stirring, 5 minutes.

Add 5 cups broth and simmer, covered, until asparagus is very tender, 15 to 20 minutes.

While soup simmers, place the tough stalks in the bottom of a sauce pan and cover with water.

Add the tips into a steamer to keep separate from tough stalks and place in same pan.

Cook reserved asparagus tips in steam salted water until just tender, 3 to 4 minutes. Reserve the stalk water.

Purée soup in batches in a blender until smooth, transferring to a bowl (use caution when blending hot liquids), and return to pan.

Stir in heavy cream, then add more broth and/or reserved stalk water to thin soup to desired consistency.

Season with salt and pepper.

Bring soup to a boil and whisk in remaining tablespoon butter.

Add lemon juice and garnish with steamed asparagus tips.