Melt the butter in a large pot or Dutch oven over medium heat. Add the chopped onion and sauté until softened and translucent, about 5 to 7 minutes.

Stir in the diced potato and cook for another 2 minutes, allowing it to coat in the butter. The potato will help thicken the soup naturally as it cooks.

Pour in the vegetable broth and bring the mixture to a gentle boil. Reduce the heat to low, cover the pot, and simmer for 10 minutes, or until the potatoes are almost tender when pierced with a fork.

Add the chopped broccoli florets and diced stalks to the pot. Cover and simmer for another 8 to 10 minutes until the broccoli is bright green and completely tender.

Remove the pot from the heat and use an immersion blender to puree the soup until smooth and creamy. Alternatively, carefully transfer the soup in batches to a countertop blender and blend, then return to the pot.

Stir in the crumbled Stilton cheese, heavy cream, and freshly grated nutmeg, letting the residual heat melt the cheese perfectly. Taste and season with salt and black pepper, keeping in mind that the cheese adds a naturally salty bite.

Ladle the warm soup into bowls and garnish with extra crumbled Stilton and a crack of black pepper. Serve immediately alongside toasted crusty bread for a deeply comforting meal.