Sauté the Aromatics: In a large, heavy-bottomed pot or Dutch oven, melt the 30g of unsalted butter over medium heat. Add the finely chopped white onion and cook for about 5-7 minutes, stirring occasionally, until it softens and turns translucent, emitting a sweet, mellow aroma. You want to see the edges of the onion just starting to turn pale gold.

Add Garlic and Create the Roux: Stir in the minced garlic and cook for another minute until fragrant; be careful not to let it brown. Then, gradually sprinkle in the 100g of plain flour, stirring constantly with a whisk. Cook for 2-3 minutes, creating a thick paste known as a roux. It should smell slightly nutty and take on a pale, sandy colour. This step is crucial for thickening the soup.

Whisk in Liquids: Slowly pour in the 1 litre of vegetable stock, whisking continuously to prevent lumps. The mixture will start to thicken almost immediately. Once smooth, gradually add the 500ml of whole milk and 250ml of double cream, continuing to whisk until everything is well combined and the mixture is silky smooth. The liquid will begin to smell wonderfully rich and dairy-like.

Simmer and Add Vegetables: Bring the soup base to a gentle simmer over medium heat, stirring frequently to prevent sticking. Once it reaches a light boil, reduce the heat to low, ensuring it's just bubbling gently. Add the 450g of finely chopped broccoli florets and the 2 medium grated carrots. Cover the pot and let it simmer for 15-20 minutes, or until the broccoli is tender when pierced with a fork but still retains its vibrant green colour. You'll notice the vegetables softening and the entire soup smelling more wholesome.

Melt the Cheese and Season: Remove the pot from the heat. This is important to prevent the cheese from seizing. Gradually add the 450g of freshly grated extra-sharp cheddar cheese, a handful at a time, stirring constantly until each addition is fully melted and incorporated before adding more. The soup will transform into a rich, golden hue and become wonderfully thick and glossy. Stir in the 1 tsp of Dijon mustard, ½ tsp of smoked paprika, and the optional pinch of nutmeg.

Final Seasoning and Serve: Taste the soup and season generously with salt and freshly ground black pepper. Adjust to your preference. The soup should taste balanced, creamy, and cheesy. Serve hot, perhaps with a sprinkle of extra cheddar or a few croutons. The warmth and aroma will be utterly irresistible.