Add everything for the tomatoes to a saucepan. Heat until the oil starts to slightly bubble and cook for 20 minutes. When the tomatoes have softened, remove from the heat and cool completely.
While the tomatoes cook, add the cheeses, basil, salt, pepper and oil to a food processor or blender. Blend until smooth. Transfer to a bowl and refrigerate.
When the tomatoes are cooled, serve them on top of the cheese. If making ahead, add the tomatoes to a container with a lid and leave at room temperature for no longer than 1 day. Refrigerate the cheese in a sealed container for up to 2 days.