1. Add 1/4 cup ice cold water and the vinegar to a glass measuring cup. Set aside.
2. In a food processor fitted with a metal blade pulse 2 cups of flour, 1 1/2 teaspoons salt, and the Mediterranean seasoning. Then add in the butter. Pulse until mixture resembles peas.
3. With the motor running, slowly add the vinegar-water through the feed tube. Process until the dough just comes together and there is no flour present. Transfer the mixture to a work surface and knead until the dough comes together- be careful not to overwork. Tightly wrap in plastic wrap, pressing to seal. Refrigerate for at least 2 hours and up to overnight.
4. Preheat the oven to 400°F.
5. Unwrap the dough onto well floured board. Let sit at room temperature while you prepare the tomatoes.
6. In a large bowl add the tomatoes and remaining 1/2 teaspoon salt. Toss to coat. Let sit at room temperature for 5 minutes, or until the tomatoes start to release some of their moisture. Drain the liquid and transfer the tomatoes to a paper towel.
7. Roll the dough into a 14-16 inch circle about an 1/8 inch thick. Move the dough to a rimless baking sheet lined with parchment paper or silicone mat. Sprinkle cheese over dough, leaving a 1 inch border. Decoratively arrange the tomato slices on top of the cheese in concentric circles or in slightly overlapping rows. Fold the pastry edge up and over the tomatoes to create a 1-inch border.
8. Brush the edges with the egg. Bake for 50-60 minutes or until the crust is golden. If using sprinkle with Celtic Sea Salt. Let cool for 15 minutes before slicing.
To move the dough by rolling it around the rolling pin and then unroll it over the parchment. A rimless baking sheet is essential for easy transfer of the galette to serving platter or cutting board.