Weigh or lightly spoon flour into a dry measuring cup, and level with a knife. Combine flour, cornmeal, butter, and ½ 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.
Preheat oven to 425°. Unwrap dough, and roll dough into a 10-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 1½-inch border. Sprinkle with the remaining ¼ 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.
Notes
Recipe from Cooking Light, very slightly modified
Recipe by Nutritious Eats at https://www.nutritiouseats.com/tomato-feta-basil-galette/