Spanish Tortilla with Manchego and Green Olives

Preheat oven to 350 degrees F. In a 10- or 12-inch ovenproof nonstick skillet over medium heat, heat 2 tablespoons oil. Add onion and 1/2 teaspoon salt, and cook, stirring occasionally, until onion is soft and translucent, 8 to 10 minutes. Transfer onion to a large bowl and set aside. In the same skillet over medium heat, heat 2 tablespoons oil. Working in batches, add half of potatoes in an even layer and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring occasionally, until potatoes begin to soften, 8 to 10 minutes. Add eggs and olives to reserved onion-potato mixture, and gently stir to combine. Wipe the skillet clean. Over medium heat, heat remaining olive oil. Add half of reserved potato-onion-egg mixture to skillet, smoothing with the back of a spoon to create an even layer. Top with cheese; then cover with remaining potato mixture, smoothing with the back of a spoon to create an even layer. Cook for 10 minutes on stovetop, then transfer skillet to oven. Bake until eggs are set and potatoes are tender, 25 to 30 minutes. Adjust oven to broil and cook tortilla until top is lightly browned, about 3 minutes. Transfer pan to a wire rack and let cool for 5 minutes. Invert onto a serving plate and cut into 6 or 12 wedges. Serve hot or at room temperature.