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Heat olive oil in a large skillet over medium heat; add guanciale (see Cook's Note). Cook, turning occasionally, until evenly browned and crispy, 5 to 10 minutes. Remove from heat and drain on paper towels.
Bring a large pot of salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until tender yet firm to the bite, about 9 minutes. Drain and return to the pot. Let cool, stirring occasionally, about 5 minutes.
Whisk eggs, half of the Pecorino Romano cheese, and some black pepper in a bowl until smooth and creamy. Pour egg mixture over pasta, stirring quickly, until creamy and slightly cooled. Stir in guanciale. Top with remaining Pecorino Romano cheese and more black pepper.