Preheat 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 atop.

Bake in the preheated oven for 1 hour. Turn tomatoes over and roast until caramelized and very soft, 1 to 1 1/2 hours. Remove from oven and set aside to cool to room temperature, about 1 hour.

Transfer tomato mixture to a blender or food processor; puree until smooth.