For The All-Purpose Galette Dough (Courtesy of Fine Cooking)
In a food processor, pulse the flour, sugar, and salt to combine. Add the butter pieces, and pulse until the mixture looks like coarse meal with some pea-sized pieces. Sprinkle with 4 Tbs. of the ice water, and pulse until the dough comes together. If too dry, add the remaining water by the teaspoon, and pulse until the dough just comes together.
Form the dough into a ball, place between two sheets of plastic wrap, and press it into an 8-inch round disc. Wrap it tightly in the plastic wrap, and refrigerate for at least 1 hour or up to 2 days before rolling out. (Or freeze it for up to 2 months; thaw in the refrigerator overnight before rolling it out.)
For The Galette Filling
Slice the tomatoes about ¼ inch thick and place on a wire rack over a baking pan. Sprinkle with salt and let sit for 30-45 minutes. Heirloom tomatoes have lots of juices and some needs to be released in order for the Galette to not be soggy.
Meanwhile, position a rack in the center of the oven and heat the oven to 400°F. Take the dough out of the refrigerator and let sit at room temperature until it is pliable, 10 to 15 minutes.
While waiting for the dough to become pliable, slice shallots thinly and set aside. In a small bowl, whisk the egg and cream and set aside.
Roll the dough between 2 sheets of lightly floured parchment paper into a 14-inch round, adding a bit more flour if it sticks. Transfer on the parchment to a baking sheet, and discard the top sheet of parchment paper.
Leaving a 2-inch border, sprinkle half of the thyme, shallots, and cheese, then layer on all of the tomatoes and sprinkle with pepper. Now sprinkle on the rest of the thyme, shallots and cheese.
Fold the edge of the dough up and over the filling, making folds as you follow the circumference of the galette. Place in the refrigerator for 10 minutes, remove and brush the folded dough with the egg wash.
Bake, rotating the baking sheet once half-way through, until the crust is golden brown, 40 to 50 minutes.
Let cool on a rack for 10 to 15 minutes. Serve warm or at room temperature.