Put the spaghetti, olive oil, 1 teaspoon salt and 5 1/2 cups of water together in a high-sided medium skillet. Bring to a boil over medium-high heat. Continue to cook, stirring the spaghetti frequently to keep it from clumping, until it is al dente, about 8 minutes. Remove from the heat and stir in the lemon juice. Gradually sprinkle in the Pecorino and stir until completely melted, then add the butter. Sprinkle in the Parmesan, pepper and 1/2 teaspoon salt and stir until melted and smooth-the cheese will clump at first but will melt into the sauce and thicken it up after about 4 minutes. Divide the spaghetti among 4 bowls and garnish with additional Pecorino and pepper.
The success of this recipe is dependent upon the specific pasta shape suggested, so we don't recommend substitutions.
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