Preheat the broiler to high with a rack set 6-inches from the heat source. Bring a large pot of salted water to a boil.
Add the pasta to the water and cook according to package directions. Drain and immediately return to the pot. Toss the pasta with the capers, raisins, red pepper flakes, and 3 tablespoons of the butter until the pasta is well coated.
Beat the eggs with the oil, 1 teaspoon salt, and a few grinds of pepper in a medium bowl. Heat the remaining tablespoon butter in a large ovenproof nonstick skillet over medium heat. Add the beaten eggs and cook, without stirring, until just set on the bottom, about 30 seconds. Then lift some of the set eggs with a spatula, letting the uncooked egg flow down to the bottom of the skillet. Repeat until the eggs are mostly set but still runny. Nestle the pasta evenly into the eggs and scatter the cheeses over the top. Broil, watching carefully, until the cheese is melted and the eggs are fully set, about 3 minutes. Cut into wedges and serve.
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