Sweat the aromatics: Melt the butter in a large stockpot over a medium heat. Add the onion, carrot, and celery, and cook for 8–10 minutes, stirring occasionally, until the onion turns translucent and the mixture smells sweet and fragrant — the carrots should have softened but not browned. The butter will take on a golden hue as the vegetables release their moisture.

Add garlic and potato: Stir in the minced garlic and the diced potato. Cook for 2 minutes, stirring constantly, until the garlic is aromatic (you'll smell a warm, pungent note) and the potato cubes begin to look slightly glossy on the edges.

Pour in the stock: Add the hot stock to the pot and bring it to a gentle boil. You should see small bubbles breaking the surface and hear a steady, bubbling sound. Reduce the heat to a simmer, cover, and cook for 10 minutes until the potato cubes are tender when pierced with a fork and the liquid looks slightly cloudy from the starch.

Cook the broccoli: Add the broccoli florets and the diced stems to the pot. Simmer uncovered for 5–7 minutes until the stems are just tender and the florets turn a bright, vivid green. The broth will take on a pale green tint, and the broccoli should still hold its shape slightly — do not overcook or the colour will dull.

Blend to a smooth consistency: Remove the pot from the heat. Using an immersion blender, purée the soup until completely smooth. The texture should look velvety and glossy, with no visible flecks of vegetable. If using a countertop blender, work in batches and remove the centre cap from the lid to allow steam to escape, covering it with a tea towel. The blended soup will have a pale, creamy green colour.

Stir in the cream and cheese: Return the pot to a very low heat. Stir in the double cream until fully incorporated — the colour will lighten to a soft, buttery shade. Add the grated cheddar a handful at a time, stirring gently in a figure-eight motion until each addition is completely melted before adding the next. The soup should thicken slightly, becoming rich and smooth, with a glossy surface and a warm, golden-amber hue.

Season and finish: Stir in the salt, pepper, and a pinch of nutmeg, if using. Taste and adjust the seasoning — you want a pronounced savoury depth with a pleasant tang from the cheese. Serve immediately, ladled into warm bowls, and garnish with a sprinkle of extra grated cheddar and a few reserved small broccoli florets if you like.