Brush one side of the pitas with olive oil. Mix the chedder and Monterey Jack cheese. Heat a cast iron skillet, remove from the heat and add one of the pitas, oiled side down. Scatter 1/2 cup of the cheese on the pita. Spoon one-fourth of the broccoli mixture over the cheese and top with another scatter another 1/2 cup of cheese. Top with another pita, oiled-side up and return the skillet to the heat. Set a small heavy skillet on top of the sandwich and cook over moderate heat until pita is browned and crisp and the cheese is melted, about 2 minutes per side. Transfer the sandwich to a work surface. Repeat with the remaining pitas, cheeses and filling. Cut the sandwiches into 4 wedges and serve right away.