Heat the butter and vegetable oil in a large saucepan, over a medium heat. Once the butter is melted, add the onions, celery and a pinch of salt to draw out the moisture and prevent the onions from browning. Cover with a lid and allow the vegetables to sweat for about 5 minutes until the onions are soft, stirring occasionally.
Add the broccoli and vegetable stock to the saucepan, bring the mixture to a boil and then down to a simmer. Cook the broccoli for 10-15 minutes or until tender.
Remove the saucepan from the heat and crumble in the blue cheese. Whizz with a hand blender or transfer into a food processor and blitz until smooth.
Season with salt and pepper to taste. Serve with croutons or with crusty bread.