In a saucepan over medium heat, drizzle in half of the olive oil. As soon as it shimmers, add the minced onions and sauté until just translucent, about 5 minutes.

Meanwhile, break the tough stems off of the asparagus. Chop into pieces reserving a few of the pretty tips for garnish.

Add in a splash of the olive oil and sauté the asparagus lightly with the onions until it is a brilliant green. Pour in the lemon juice. Transfer to a blender, pour in the broth and blend until smooth. If you want it even smoother, pour through a wire mesh sieve or strainer.

While you blend the soup, lightly saute any asparagus tips in a splash of olive oil, just until bright green.

For hot soup, return the soup to the pot and bring up to a simmer. Taste. Season with the salt and pepper.

For chilled soup, season with salt and pepper. Place in the freezer for 20 minutes, stirring periodically. Alternatively, prepare a large bowl of ice water. Place the smaller bowl with the asparagus soup in the ice bath, stir periodically until chilled. If you are making well in advance it can also chill out in the fridge for 4-6 hours.