Preheat the oven to 300 degrees F.
Put a cooling rack over a baking sheet. Slice the tomatoes, horizontally, into thirds and arrange the slices on the rack. Put the top and bottom of the tomatoes, cut side up, on the rack. Dress the tomatoes with a little extra-virgin olive oil, season with salt and pepper, to taste, and a little fresh thyme. Roast the tomatoes for 1 hour. Remove the tomatoes from the oven and arrange them on a serving platter.