Preheat the oven to 425°F.
Put 3 tablespoons of oil into a large, oven-safe sauté pan or large skillet, for which you have a lid, on medium heat to medium-high heat. Add the onion and cook for 8 minutes, stirring occasionally, until softened and browned.
Add the garlic, Chile flakes, and anchovies and cook for 1 minute more, until fragrant.
Stir in the capers, half the preserved lemon, ⅓ cup/45g of olives, the tuna, tomato paste, canned tomatoes, orzo, 1¾ cups/450ml of water, 1 teaspoon of salt, and a generous grind of pepper.
Bring to a simmer, then cover with the lid and bake for 20 minutes, until the orzo is cooked through.
Turn the oven temperature up to 475°F. Remove the lid, top with the sliced tomatoes, sprinkle with the cheese, and bake for 10-12 minutes more, until lightly browned. Let sit for 10 minutes.
Top with the remaining olives and preserved lemon, garnish with the basil leaves, and the remaining 1 tablespoon of oil.