Step 1
Combine flour cornmeal salt and frozen butter in a food processor. Pulse until mixture resembles coarse crumbs. Add vinegar and ice water and pulse again until mixture comes together in clumps scraping down the sides of the bowl as needed.
Step 2
Wrap dough up in plastic wrap and shape into a disc. Refrigerate until thoroughly chilled about 1 hour.
Step 3
Combine goat cheese egg yolk kosher salt pepper cayenne and basil in a bowl. Mix using a spatula until smooth and soft.
Step 4
Place dough on a lightly floured work surface and sprinkle top with flour. Roll out into 1/8-inch-thick circle about 13 inches in diameter. Roll dough over the rolling pin and transfer onto a 12-inch pizza pan; refrigerate until ready to use.
Step 5
Preheat the oven to 425 degrees F (220 degrees C).
Step 6
Mix tomatoes 1 tablespoon olive oil and Dijon mustard together in a bowl.
Step 7
Drop spoonfuls of the cheese mixture onto the dough and spread evenly leaving about 1 1/2-inch space on the sides. Place tomato mixture on top of cheese using a slotted spoon. Fold excess dough up and over tomatoes creating a pleat every 3 inches or so by gently pressing and folding.
Step 8
Combine beaten egg and water in a small bowl; brush over crust. Sprinkle Parmigiano-Reggiano cheese over galette.
Step 9
Place a foil-lined pan on the rack under galette to catch any possible drips. Bake in the preheated oven until well browned on bottom and top 30 to 35 minutes.
Step 9
Remove from the oven and let cool completely about 30 minutes. Sprinkle with remaining olive oil and sea salt. Serve room temperature or chilled.