1. Weigh or lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour, cornmeal, butter, and 1/2 teaspoon salt in a food processor; process until the mixture resembles coarse meal. With processor on, slowly add ice water through food chute, and process just until combined (do not form a ball). Gently press the mixture into a 4-inch circle on heavy-duty plastic wrap. Cover and chill for 30 minutes.
2. Preheat oven to 425°.
3. Unwrap dough, and roll dough into a 13-inch circle on a lightly floured surface. Place dough on a baking sheet lined with parchment paper. Arrange tomatoes, cut sides up, on top of dough, leaving a 1 1/2-inch border. Sprinkle with the remaining 1/4 teaspoon salt and pepper. Fold edges of dough over tomatoes to partially cover. Bake at 425° for 25 minutes or until golden brown. Sprinkle evenly with cheese. Bake an additional 5 minutes. Cool for 5 minutes, and sprinkle with basil. Cut into 8 wedges.