Step 1

Slice the florets off the heads of broccoli, rinse in a strainer, and set aside.

Step 2

With a vegetable peeler, remover the tough outer woody layer from the broccoli stems and finely dice the tender green inner stems.

Step 3

Heat the olive oil in a medium (3- to 4-quart) stockpot or Dutch oven over medium low heat.

Step 4

Add the broccoli stems and onion and cook, stirring occasionally, for about 5 minutes until the vegetables are translucent and tender.

Step 5

Stir in the carrot and 1/4 teaspoon salt and cook for 1 to 2 minutes more until the carrot is softened. Add the Parmesan rind and vegetable broth. Cover the pot and increase the heat to medium. Bring to a boil, then uncover and reduce the heat as needed to keep the broth at a simmer. Cook for 30 minutes, then remove the Parmesan rind with tongs or a slotted spoon.

Step 6

Add the milk and heat until the soup returns to a simmer. Toss the shredded cheese with the cornstarch and mustard powder in a small bowl, then stir into the soup until melted. Add half the reserved broccoli florets and cook for 5 minutes until tender.

Step 7

Remove the soup from the heat. Carefully purée the soup with an immersion blender or countertop blender for 10 to 15 seconds, just until the florets break up.

Step 8

Return the soup to the pot and bring back to a simmer. Add the remaining broccoli florets and cook for 5 minutes until tender. Taste and season with salt and pepper, as needed. Serve immediately.