Prepare all of the ingredients before beginning.
Cut off the woody ends of the asparagus and discard. Wash and then chop the asparagus stalks into roughly one-inch pieces. Set aside.
Mince one clove of garlic and set aside.
Zest the lemon and then squeeze one tablespoon of juice.
Dice the chives. Set aside.
Melt the butter/heat the olive oil in a Dutch oven or large pot over medium-high heat.
Add the garlic and cook one minute, stirring. Do not let the garlic brown. If it is cooking too quickly, lower the temperature to medium heat.
Add the asparagus pieces, chives, lemon zest, and lemon juice to the garlic.
Pour in the chicken broth and bring to a vigorous simmer.
Cook, stirring occasionally, until the asparagus are fork tender, about 15-20 minutes.
Remove the pot from the heat and pour in the heavy cream in a steady stream while stirring.
Blend to the desired consistency. See Tips & Tricks for help with blending.
Add a pinch of salt and some fresh black pepper.
Top with a dollop of crème fraîche or sour cream, diced chives, and a snip of fresh dill.