Toss tomatoes with thyme, oil and salt. Arrange on a parchment lined backing sheet, cut side down and roast for 1 ½ hours at 300 F.
Turn tomatoes right side up and sprinkle with chopped garlic. Then roast for another 30 minutes until they are shriveld and browned around the edges.
Once cooled, remove tomato skins, and puree tomatoes in a food processor. Add butter, basil, vinegar, salt and pepper and blend until combined.
Place oysters on a baking sheet, and top each one with ½ teaspoon of tomato butter. Broil 5-10 minutes until butter is bubbling, and the edges of the oysters begin to curl.