Sweat the aromatics: Heat the olive oil in a small frying pan over a medium heat. Add the diced onion and cook for 4-5 minutes until it becomes translucent and fragrant. Stir in the minced garlic and cook for a further 30 seconds until you can smell that sharp, pungent aroma. This brief sauté unlocks the sweetness of the onion and removes the raw bite of the garlic, building a deeper flavour base for the soup.

Build the base: Transfer the cooked onion and garlic to the slow cooker. Pour in the chicken stock, then add the chopped broccoli (florets and stalk), diced potato, carrots, dried mustard powder, and smoked paprika. Give everything a good stir. The potato is our secret weapon here – as it breaks down during the long cooking time, it releases its natural starches, which thicken the soup without needing a flour-based roux.

Slow cook: Place the lid on the slow cooker and cook on high for 3 hours, or on low for 6 hours. You'll know it's ready when the broccoli is fork-tender and the potato cubes crumble easily when pressed against the side of the pot. The liquid should look slightly cloudy and reduced.

Blend until smooth: Using an immersion blender, carefully blend the soup directly in the slow cooker until it reaches your desired consistency. I prefer a mostly smooth soup with a few tiny flecks of broccoli for texture, but you can blitz it until it's completely velvety if you prefer. If you don't have an immersion blender, carefully transfer the soup in batches to a stand-up blender, filling it no more than halfway to avoid hot splashes.

Add the dairy: Pour in the whole milk and stir well. The colour will shift from a dull greenish-yellow to a paler, creamier shade. Let the soup cook for another 10 minutes on high to warm the milk through completely.

Melt the cheese: Reduce the slow cooker to the 'warm' setting. Add the freshly grated cheddar cheese by the handful, stirring gently after each addition until it has fully melted. You'll see the soup transform into a glossy, golden-orange river of cheese. Do not let the soup boil at this stage, as high heat can cause the cheese to separate and become greasy.

Season and serve: Taste the soup and season generously with salt and freshly cracked black pepper. Remember that cheese is already salty, so add the salt in small increments. Ladle the soup into bowls while it's steaming hot and glossy.