Heat olive oil and butter in a saucepan over medium-high heat. Toss with a spoon every few minutes until the tomatoes release their liquid and start to break down. Bake in the preheated oven until the cheese is well browned and crispy around the edges, 15 to 20 minutes. Remove soup from heat and pass through a mesh strainer into a bowl. Use the back of a ladle to push all the tomato mixture through.
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