Remove the lid and stir in the evaporated milk. With an immersion blender, puree about 3/4 of the soup, so that it is mostly smooth but still has a few chunks of broccoli remaining. Alternatively, you can puree the soup in 1 cup-sized batches in a food processor or blender. (Be careful—it’s hot and prone to splatter!)
Recover the soup and let cook on low for 10 minutes until warmed through. Stir the salt, pepper, and grated cheese. Taste and add additional salt and pepper as desired. Recover and cook on high until the cheese is fully melted and the soup is hot, about 5 additional minutes. Serve warm.
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