Preheat the oven to 425 degrees F. Heat 2 tablespoons olive oil in a large nonstick skillet over medium-high heat. Add the onion and cook, stirring occasionally, until lightly browned, about 5 minutes. Add 3 minced garlic cloves and cook until softened, about 30 seconds. Stir in the ras el hanout. Add the beef and season with salt and pepper. Cook, stirring and breaking up the meat, until browned, 5 to 7 minutes. Add the tomatoes and chickpeas with their liquid and bring to a boil. Reduce the heat to a steady simmer and cook until slightly thickened, 10 to 12 minutes. Season with salt and pepper.
Meanwhile, combine the spinach, cheese, remaining 1 tablespoon olive oil and 2 minced garlic cloves in a bowl; season with salt. Stuff the mixture into the pita halves, wrap each in foil and transfer to a baking sheet. Bake until the cheese is melted, about 10 minutes.
Divide the stew among bowls; top with cilantro. Serve with the spinach pitas.