1. To make the dough, combine flour, sugar, cornmeal, and salt in a processor; pulse 2-3 times. Add butter and pulse 4-5 times, or until mixture resembles coarse meal. With the processor running, slowing pour the buttermilk through the chute, processing until the dough forms a ball. Remove the dough ball and adhere any remaining pieces of dough to it, then wrap in plastic wrap or parchment paper. Refrigerate for at least 45 minutes before rolling out.
2. Center a rack in the oven and preheat to 350 degrees F. Remove the galette dough from the refrigerator and place on a sheet of parchment paper. Starting at the center of the dough, roll out, forming a 14-15-inch wide circle. Place the dough with parchment paper on a baking sheet.
3. Slice the heirloom tomatoes and place them on paper towels. Brush the galette dough with pesto. Place the tomato slices on top of the dough, leaving a 2-inch border. Fold the dough border over the tomatoes, overlapping where necessary and pressing gently to adhere the folds. Lightly brush the edge of the dough with the beaten egg.
4. Bake the galette for 45 minutes, or until the crust is golden brown. Transfer the baking sheet to a wire rack to cool to room temperature before slicing. Slice and serve.
*Note-you can make the galette dough in advance. It will keep in the refrigerator for 3 days. You can use store-bought pesto if you are in a pinch, but we like to use our Spinach Basil Pesto. And any heirloom tomatoes will work for this recipe!