In a food processor, combine the sun-dried tomatoes with the olives and oregano. Season with pepper and process to a coarse paste.
Lightly brush 1 side of each slice of bread with olive oil and set on a large baking sheet, oiled side down. Top half of the bread with the provolone, spread each slice with 1 tablespoon of the tomato-olive pesto and top with the mozzarella. Close the sandwiches with the remaining bread, oiled side up.
Heat a griddle or a very large skillet. Arrange 3 or 4 sandwiches on the griddle and top with a cast-iron skillet: do not press the pan down. Cook the sandwiches over moderately high heat until golden on the bottom, about 2 minutes. Flip the sandwiches and cook until browned and the cheese is melted, about 2 minutes longer. Transfer to a wire rack to cool. Repeat with the remaining sandwiches.
Cut the crusts off the sandwiches, then cut into triangles and serve.
MAKE AHEAD The panini can be prepared through Step 3 and stored on a wire rack at room temperature for up to 6 hours. Reheat on a baking sheet in a 350°F oven until crisp.