Broccoli Cheese Soup Recipe

Separate broccoli into florets and stems. Cut florets into bite-size pieces and set aside. Roughly chop stems and reserve separately.
Heat oil in a large Dutch oven over high heat until shimmering. Add broccoli florets and cook, without moving, until charred on the bottom, about 1 minute. Stir, season with salt and pepper, and continue cooking, stirring occasionally, until tender and charred on several surfaces, about 1 minute longer. Transfer to a rimmed baking sheet to cool.
Return Dutch oven to medium heat and add butter, onion, carrot, and broccoli stems. Season with salt and pepper and cook, stirring frequently, until tender but not browned, about 5 minutes, lowering heat if necessary. Add garlic and cook, stirring, until fragrant, about 30 seconds.
Add water or chicken stock, milk, and potato and bring to a boil over high heat. Reduce to a bare simmer and cook, stirring occasionally, until broccoli and potato are completely tender, about 30 minutes.
In a large bowl, toss both cheeses together along with mustard powder. Using an immersion blender or working in batches with a countertop blender, blend soup, adding cheese a handful at a time, until completely smooth. Stir in hot sauce and season to taste with salt and pepper. Stir in reserved broccoli florets and pulse with blender a few more times until a few pieces are broken down, but most bite-size pieces remain. Serve immediately.