Step 1Cut each tomato into 4 to 6 slices. In a large bowl, combine the sliced tomatoes with the oil, oregano, garlic, olives, salt and several grinds of black pepper, tossing well to mix.
Step 2Heat the oven to 400 degrees. Remove the dough from the refrigerator to a flat surface lined with a lightly floured sheet of parchment. Roll the dough into a rough circle about 15 inches in diameter and a generous one-eighth-inch thick. Transfer the dough (still on the parchment) to a baking sheet.
Step 3Gently spoon the tomato mixture into the center of the dough. Fold the outer 3 inches of the dough circle toward the center to make a packet, leaving the inner 4 or 5 inches of tomatoes uncovered (the assembled galette will be about 9 inches in diameter). Lightly brush the outer edge of the pastry with the beaten egg.
Step 4Bake until the crust is golden-brown and the tomatoes are softened, about 45 minutes. Start checking the galette after 30 minutes, and loosely cover the tomatoes with a sheet of foil if they color too quickly. Cool the galette 15 to 20 minutes before slicing, and scatter a little fresh basil over each slice before serving.