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1
In a medium bowl, mix together the flour, cornmeal, sugar, and salt. Cut in the chilled butter using a stand mixer, a food processor, or a pastry blender until it's evenly distributed but still in large, visible pieces. Add the olive oil and ice water and mix until the pastry begins to come together. Gather the pastry with your hands and shape it into flattened round. Shape into 2 flattened rounds for 2 small galettes or 1 flattened round for 1 large galette. Wrap the pastry in plastic wrap and refrigerate for 1 hour. If refrigerated longer, let pastry soften slightly before rolling. Can be made ahead and refrigerated up to 3 days.
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2
While pastry firms in refrigerator, slice the tomatoes about 1/4-inch thick, lightly salt and spread on paper towels to drain. Let set and blot off excess moisture.
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3
Place oven rack to the center position and preheat the oven to 375u00b0F.
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4
On a large piece of parchment paper which as been lightly sprinkled with cornmeal, roll the dough into a 15-inch round. Place the parchment paper with dough onto a baking sheet. If your baking sheet has sides, flip it over and use the back so that all sides of galette will brown. Trim off excess parchment paper that hangs past the sides of the baking sheet. Lift the sides of the dough with a metal spatula to make sure it's not sticking.
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5
Sprinkle gruyere cheese over the dough, leaving a 2-inch border without filling. Sprinkle basil over cheese. Arrange the tomato slices in a single layer over cheese and basil. Brush the tomatoes with a little olive oil and season with freshly ground black pepper. Fold the flaps of extra dough inward over the tomatoes, pleating as you go, to form a folded-over border. Pinch together any tears in the dough. Brush exposed crust with egg whites.
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6
Bake until the crust is golden brown about 35 to 45 min. Slide the galette off the parchment and onto a cooling rack. Let cool for 10 minutes. Cut the tomato gruyere galette into wedges and serve warm or at room temperature.
