Mash together the cheese and butter in a small bowl. Season with peppers and stir in the chives. Shape into a short cylinder, no more than 5cm (2in) in length, and wrap in clingfilm. Chill for at least an hour to firm up.
Divide the beef into fout portions. Using wet handsm shape into round patties 2.5cm (1 in) thick, remove the blue cheese butter from the fridge and cut into four even-sized pieces. Make a deep indentation in the middle of each patty and insert a piece of butter, pushing the beef around it until it is completely enclosed. Chill for at least an hour or up to 24 hours until ready to cook.
Preheat the grill to its highest setting or, if using a charcoal barbeque to cook the burgers, light it 30 minutes before you want to start cooking. If using a gas barbeque, light it 10 minutes beforehand. Also preheat the oven to 200c/400F/gas mark 6. Snip the tomatoes into four portions of three and arrange in a small roasting tin. Drizzle with 1 tablespoon of the olive oil and season with salt and pepper. Roast in the oven for 12-15 minutes until lightly charred and just beginning to soften.
Sprinkle a teaspoon of pepper all over the chilled burgers. Put on the grill rack and cook for 4 minutes on each side for rare, 6 minutes for medium and 8-9 minutes for well done.
To make a dressing, mix the remaining olive oil with the lemon juice and sweet chilli sauce. Place the parsley and red onion in a separate bowl and then fold in two-thirds of the dressing.
To serve, toast the muffin halves on the grill rack and place on warmed plates. Put a burger on each muffin half and then add a bunch of roasted tomatoes. Pile the red onion salad on top and drizzle with the remaining dressing.