1medium carrotabout 4 ounces; 120g, peeled and finely diced
3medium cloves garlicthinly sliced
2cupswater475ml, or low-sodium chicken stock
3cupswhole milk700ml
1small russet potatoabout 4 ounces; 120g, peeled and sliced
12ouncessharp cheddar cheese340g, see note above, grated
8ouncesdeli-style American cheese240g, see note, diced
1teaspoonmustard powder3g
Dash of hot saucesuch as Frank's RedHot
Instructions
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 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.
Notes
Look for deli-style American cheese at the deli counter of your supermarket. You can use any combination of cheddar, American, and other young, moist cheeses, like Jack or Colby.