Chop the broccoli into small florets - if using frozen broccoli, let it thaw slightly first. Dice the potato and onion, and mince the garlic.
Heat the olive oil or butter in a large saucepan. Add the onion and garlic and cook until softened and fragrant, about 5 minutes.
Stir in the potato and broccoli florets, then pour in the stock and bring to a gentle boil.
Reduce the heat and simmer for 15-20 minutes, until the potato and broccoli are completely tender. Blend until smooth.
Return the blended soup to the pan over low heat. Stir in the cream and crumbled Stilton, allowing it to melt gently - do not let the soup boil.
Taste and season with salt and pepper as needed. Ladle into bowls and top with your choice of garnish.