Position a rack in the upper third of the oven; preheat to 425 degrees .
Grease a small rimmed baking sheet liberally with butter. Place 4 slices of bread on the baking sheet, arranging them next to each other to form a large square.
In a medium skillet, heat the olive oil, two turns of the pan, over medium. Add the scallions, garlic and chile; stir until the mixture softens, about 2 minutes. Scatter the scallion mixture evenly over the bread; top with an even layer of sliced tomatoes. Season with the oregano, salt and pepper. Top the tomatoes with remaining bread to form sandwiches that are arranged tightly together like a Sicilian pizza.
In a small bowl, beat the eggs and milk; season. Pour the egg mixture evenly over the bread. Top with the provolone. Bake the sandwiches until golden and heated through, 18 to 20 minutes.
In a medium bowl, toss the greens with the lemon juice and EVOO; season. Serve the sandwiches with the greens.