Build the aromatic base: Melt the butter in a large, heavy-bottomed pot over a medium heat. Once the butter has fully melted and begins to foam gently—you'll hear a soft, contented sizzle—add the diced onion. Stir frequently for 5 to 7 minutes, until the onion turns translucent and releases a sweet, mellow fragrance. The pieces should look softened but not browned. Add the garlic and stir for a further 30 seconds, until it smells fragrant and warming.

Create the golden roux: Sprinkle the flour over the softened onion mixture and stir continuously with a wooden spoon for 2 minutes. The mixture will clump and look like a thick, sandy paste. Keep stirring until the raw flour smell fades and a faint, nutty aroma rises from the pot. The roux should be a pale golden colour—this is the foundation of your soup's velvety texture.

Whisk in the liquid: Slowly pour in the chicken stock while whisking vigorously to prevent lumps. The mixture will thicken almost immediately and look like a thin, lumpy gravy. Continue whisking for a full minute until smooth. Follow with the milk and double cream, whisking constantly. Bring the liquid to a gentle simmer—you'll see tiny bubbles breaking the surface, but do not let it boil aggressively or the dairy may split. Lower the heat if necessary.

Simmer the vegetables: Add the finely chopped broccoli stalks and the grated carrot. These need longer to soften than the florets. Stir in the smoked paprika, nutmeg, and a generous pinch of salt and pepper. Let the soup simmer gently for 10 minutes, stirring occasionally. The colour will deepen to a pale, creamy green, and the aroma will become wonderfully savoury with a hint of warm spice.

Add the broccoli florets: Tip in the broccoli florets and continue simmering for another 5 to 6 minutes. You're looking for the stalks to be tender enough to pierce with a fork, while the florets remain a vibrant, bright green and offer slight resistance when bitten. At this stage, the soup will look fairly thin—do not worry, the cheese will thicken it beautifully.

Melt in the cheese: Remove the pot from the heat entirely. It is crucial to let the soup cool for 1 to 2 minutes before adding the cheese—excessive heat causes cheddar to become greasy and stringy. Sprinkle the grated cheese into the pot by the handful, stirring gently after each addition. Watch as the cheese melts into golden ribbons that disappear into the soup, leaving behind a thick, glossy, sunset-orange finish. The surface should be smooth and unbroken, with a rich, creamy sheen.

Final seasoning and rest: Taste the soup carefully (it will be hot) and adjust the salt, pepper, and cayenne if using. I find a tiny pinch of cayenne lifts the richness without adding noticeable heat. Let the soup rest off the heat for 5 minutes before serving. During this time, the flavours meld together, and the texture settles into a luscious, spoon-coating consistency. Give it one last gentle stir before ladling into bowls.