Preheat the oven to 250 degrees F (120 degrees C).
Arrange tomatoes, cut-side up, in a shallow baking dish; drizzle with olive oil and sprinkle garlic, oregano, sugar, and salt evenly on top.
Bake in the preheated oven for 1 hour.
Turn tomatoes over and continue baking until caramelized and very soft, 1 to 1 1/2 hours. Remove from the oven and set aside to cool to room temperature, about 1 hour.
Transfer tomato mixture to a blender or food processor; purée until smooth.