First, make the tart crust. In a large bowl, place the flour, xanthan gum and salt, and whisk to combine well. Add the chopped and chilled butter, and toss to coat the butter in the dry ingredients. Press each floured chunk of butter between a floured thumb and forefinger to flatten.

In a small bowl, whisk the egg yolk (reserve the white) and 1/2 cup cold water until well combined. Create a well in the center of the large bowl of dry ingredients, add the egg yolk and water mixture and mix to combine. The dough will come together.

Transfer the dough to a large piece of plastic wrap. Cover and press into a disk. Refrigerate for at least 2 hours or up to overnight.

Once the dough has chilled, preheat your oven to 400°F. Grease the bottom and sides of a 12-inch tart pan with a removable bottom and set it aside.

Turn the dough out onto a well-floured surface. Dust the surface with a bit more flour, and roll it out with a rolling pin into a 1/2-inch thick rectangle. Fold the rectangle in half lengthwise, dust again lightly with flour, and roll the dough out again into a 1/2-inch thick rectangle.

Once more, fold the rectangle in half lengthwise, and then fold again widthwise to create a thick square. Dust the square lightly with flour, and roll the dough out into a round that is about 14-inches in diameter.

Transfer the round of dough to the prepared tart pan, and press it gently into the bottom and the sides of the pan. Trim the edges of the dough flush with the upper edge of the sides of the pan.

Pierce the bottom of the tart crust with the tines of a fork about 20 times. Brush the bottom surface of the crust generously with the egg white. Place the crust in the freezer until firm (about 5 minutes).

Once the crust has chilled, remove it from the freezer, and fill it. Scatter about half of the grated cheese in an even layer over the bottom of the crust. Place the tomato slices in a tight but even layer on top of the grated cheese. Scatter the basil leaves on top of the tomatoes.

Drizzle the filling evenly with the olive oil, sprinkle evenly with the salt, and cover with the remaining grated cheese in an even layer. Place the tart pan on a rimmed baking sheet lined with parchment paper.

Place the baking sheet with the tart on it in the center of the preheated oven. Bake for 10 minutes. Reduce the oven temperature to 350°F, and continue to bake until the tomatoes are soft, and the crust is an even, golden brown (about another 25 minutes).

Remove the tart from the oven and allow it to cool for 15 minutes before removing it from the tart pan. Slice and serve at warm room temperature.

The tart can be covered and refrigerated for a couple days before serving. Warm in a 250°F oven before serving.