Preheat oven to 400°. Whisk together first 5 ingredients in a large bowl. Toss tomatoes in olive oil mixture, and place on a broiler pan.
Arrange cheese sticks, cut sides up, on a lightly greased 15- x 10-inch jelly-roll pan.
Bake cheese sticks and tomatoes, at the same time in separate pans, at 400° for 15 minutes or until cheese sticks are lightly golden and tomatoes begin to burst, stirring tomatoes occasionally.
Place cheese sticks on a platter. Spoon tomatoes and any accumulated liquid over cheese. Sprinkle with basil. Serve immediately.
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