Preheat the oven to 180°C.
Score around the top of the cheese boxes and remove the top layer of skin.
Drizzle the cheeses with oil and bake for 15-20 minutes until melted.
Fry butter, brioche crumbs, and thyme until golden-brown and top the baked cheese.
Preheat a deep-fat fryer to 190°C and boil 125ml of water with butter.
Beat in the flour until the mixture is smooth and leaves the pan sides.
Cook the flour mixture over heat for two minutes.
Incorporate the eggs one at a time, beating well.
Mix in the crumbled Stilton and season with salt and pepper.
Fry teaspoonfuls of batter for 2-3 minutes until golden and crisp.
Drain the beignets on kitchen paper and season with salt.
Boil the seasonal vegetables until tender and drain.
Serve the baked cheese with beignets and vegetables on the side.