For the baked reblechon cheese, preheat the oven to 180C/350F/Gas 4.
Leave the cheese in the boxes and score around the top about 5mm/¼in in and cut off the top layer of skin.
Drizzle the oil over the cheeses and place in the oven for 15-20 minutes, or until oozy in the middle.
In the meantime, heat a large frying pan and, once hot, add the butter. Add the breadcrumbs and thyme to the pan and cook until golden-brown and toasted. Top the cheese with the breadcrumbs.
For the deep-fried blue cheese beignets and seasonal vegetables, preheat a deep-fat fryer to 190C/375F. (CAUTION: hot oil can be dangerous. Do not leave unattended.) Place 125ml/4fl oz water and the butter into a saucepan and bring to a rolling boil for a minute.
Remove the pan from the heat and add the flour, beating well until the mixture is smooth and comes away from the sides of the pan.
Return to the heat for a minute or two to cook the flour out.
Remove from the heat again and add the eggs, one at a time, beating well between the addition of each egg.
Add the crumbled Stilton and mix well. Season with salt and freshly ground black pepper.
Drop teaspoonfuls of the batter into the deep-fat fryer and fry for 2-3 minutes, or until golden-brown and crisp (you may need to do this in batches).
Remove the beignets from the oil with a slotted spoon and set aside to drain on a plate lined with kitchen paper. Season with a little salt.
Meanwhile heat a large saucepan of boiling water and cook the vegetables to your liking. Drain.
To serve, place the baked cheeses on a large serving plate and place the beignets and vegetables alongside.