Preparation Steps

• Prep the ingredients: shred the cheddar, finely chop the onion, mince the garlic, and cut the broccoli into small florets (peel and finely chop the tender stems). Warm the half-and-half in a microwave-safe cup for 45–60 seconds to take the chill off; set aside.
• Start the vegetables in broth: bring the chicken broth to a gentle simmer in a medium saucepan. Add the chopped broccoli stems and the carrots. Simmer 6–8 minutes until just tender-crisp; keep warm over low heat.
• Build the base: in a Dutch oven over medium-low heat, melt the butter. Add the onion and garlic with a pinch of salt and cook 5 minutes, stirring occasionally, until soft and translucent without browning.
• Make a blond roux: sprinkle in the flour and cook, stirring, for 2–3 minutes until it smells nutty and looks foamy.
• Thicken with broth: while whisking, slowly stream in the hot broth with the carrots and stems. Bring to a gentle simmer and cook 5 minutes to thicken slightly.
• Add the florets: stir in the broccoli florets and cook at a low simmer for 8–10 minutes, until the broccoli is tender but still bright green.
• Creamy finish before cheese: stir in the warmed half-and-half and the Dijon. Season with salt and black pepper. Keep the heat on low and let it gently bubble for 2–3 minutes.
• Choose your texture: blend about half the soup with an immersion blender right in the pot, leaving plenty of pieces for texture. (Or transfer 2 cups to a blender, vent the lid, blend until smooth, and return to the pot.)
• Off heat, add the cheddar by the handful, stirring until fully melted and smooth. If the soup seems too thick, thin with a splash of warm broth or half-and-half.
• Let the soup rest 5 minutes, then taste and adjust seasoning before ladling into bowls.