Halve the cherry tomatoes and arrange in a baking pan with the cut surface facing up.
Add thyme to a mortar and mash well. Then, add oil and mash for about 20 seconds.
Sprinkle the tomatoes with sugar, salt and pepper, and drizzle with a little oil. Bake the tomatoes at 225°F for about 2 hours.
Arrange the tomatoes on grilled bread and top with plenty of grated Aged Havarti or Cheddar and finish with a drizzle of the remaining oil.