On a lightly floured surface, roll out pate brisee to 1/8 inch thick. Using a paring knife, cut out twelve 4 1/2-inch squares, and fit into cups of a standard muffin tin, leaving an overhang. Refrigerate for 30 minutes.
Preheat oven to 400 degrees. Divide tomato and onion slices between 2 rimmed baking sheets. Drizzle with oil, season with salt and pepper, and roast, switching positions of sheets halfway through, until tomatoes begin to shrivel and onion slices are golden, about 30 minutes. Let cool. Transfer to a bowl.
Divide half the chopped oregano, olives, and feta among the dough-lined tins. Top with tomato-onion mixture. Sprinkle remaining oregano, olives, and feta on top. Fold corners of dough toward centers. Brush with egg wash.
Reduce heat to 375. Bake pies until top crusts are golden brown and middles are bubbling, 50 to 60 minutes.
Let cool completely in tin on a wire rack. Tuck oregano sprigs into hand pies if desired.