01 -
Melt butter in a large Dutch oven over medium-low heat. Add onions, garlic, red pepper flakes, ¼ teaspoon salt, and black pepper. Cover and cook until onions soften and turn slightly golden, about 8-10 minutes, stirring occasionally.
02 -
While aromatics cook, trim broccoli stalks and peel tough outer skin. Cut stalks into 1-2 inch pieces and set aside. Cut florets from stalks, keeping them separate - we'll use them at different times.
03 -
Add broccoli stalk chunks and potato to the pot with 6 cups water and remaining 1 teaspoon salt. Bring to a boil, then reduce heat, cover, and simmer until stalks and potatoes are fork-tender, about 20-25 minutes. Meanwhile, chop reserved florets into small pieces.
04 -
Once potato and stalks are tender, add half the florets to the pot. Stir, cover, and cook until bright green, about 3-5 minutes. Remove from heat.
05 -
Working in batches (careful not to overfill!), transfer mixture to a blender and purée until completely smooth. Return puréed soup to the pot. Alternatively, use an immersion blender for a slightly less creamy texture.
06 -
Return pot to medium heat and add remaining florets. Cover and cook until bright green and tender, 4-7 minutes more.
07 -
Stir in most of the cheddar cheese until melted and smooth, reserving a small handful for garnish. Taste and adjust seasonings, adding more cheese for richness, salt for flavor, or black pepper for kick.
08 -
Ladle soup into bowls and top with reserved cheese, chives, and/or red pepper flakes if desired. Soup keeps well refrigerated for up to 4 days, though the color may darken slightly.