Step 1

Heat the olive oil in a large pot over medium-low heat. Add the shallots and gently cook, stirring occasionally, until soft and translucent, 8 to 10 minutes. Do not brown.

Step 2

Add the vegetable broth, peas, salt, and pepper. Bring to a boil, then reduce the heat to medium-low and cook, uncovered, for 10 minutes.

Step 3

Remove the pan from the heat, then add the basil, Parmigiano-Reggiano, and lime juice. Purée with a stick blender until smooth and creamy. Be patient; you want it as smooth as possible. (If you don’t have a stick blender, let the soup cool slightly and purée it in batches in a blender. Be sure to crack the lid or remove the center cap to allow the steam to escape and cover with a dish towel so it won't splatter.) Taste and adjust the seasoning, if necessary. Ladle the soup into bowls and serve with more basil, if desired. (Alternatively, chill the soup and serve cold.)

Step 4

Note: This soup will thicken as it cools. If necessary, add a bit of water to thin to desired consistency.

Step 5

Freezer-Friendly Instructions: The soup can be frozen for up to 3 months. When ready to serve, defrost overnight in the refrigerator and then reheat on the stovetop over medium heat until hot.