Step 1 Cut 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 2 Heat 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.