Sweat the aromatics: Melt the butter in a large stockpot over a medium-low heat. Add the onion, carrot, and celery. Cook for 8–10 minutes, stirring occasionally, until the vegetables are soft and translucent but not coloured. You'll know they're ready when the kitchen smells sweet and the onions look glossy.

Bloom the garlic and spice: Stir in the minced garlic and smoked paprika. Cook for one minute until the garlic is fragrant – you'll smell it release its aroma immediately.

Make the roux: Sprinkle the flour over the vegetables and stir constantly for 2 minutes. The mixture will look like a sandy paste. Cook until it turns a pale golden colour and smells slightly toasty, like a biscuit.

Add the stock slowly: Pour in the stock in a steady stream, whisking continuously to prevent lumps. The mixture will thicken quickly at first, then loosen as you add more liquid. Bring it to a gentle simmer – you'll see small bubbles breaking the surface.

Cook the broccoli: Add the chopped broccoli stalks and florets. Simmer for 12–15 minutes, uncovered, until the stalks are tender enough to pierce easily with a fork. The colour will deepen to a vibrant dark green.

Blend until velvety: Remove the pot from the heat. Use an immersion blender to puree the soup until completely smooth. If you don't have one, carefully transfer the soup in batches to a blender and blend until silky. The texture should be thick and glossy.

Finish with dairy and cheese: Return the pot to a low heat. Stir in the milk and double cream until combined. Add the grated cheddar a handful at a time, stirring gently until each batch is fully melted before adding the next. The soup will turn a rich, pale gold and smell intensely of cheese.

Season and serve: Stir in the salt, pepper, and nutmeg, if using. Taste and adjust the seasoning – you might want a little more salt to lift the flavours. Ladle into bowls and serve immediately.