For the gnocchi: In a large bowl, combine the mascarpone, egg, egg yolk, nutmeg, lemon zest, Parmesan, and salt. Using a hand mixer, beat on medium speed until light and fluffy, about 1 minute. Gradually beat in 3/4 cup flour until the mixture forms a soft dough.
Sprinkle a pie pan or rimmed baking sheet with flour. Using 2 small spoons, drop 1 teaspoon-sized pieces of dough into the pie pan. Shake the pan gently to cover the dough with flour. Gently roll the pieces of dough into oval shapes.
Bring a large saucepan of salted water to a simmer. In batches, carefully add the gnocchi. The gnocchi should sink and then float to the top. As soon as the gnocchi begin to float, cook for 5 to 6 minutes. Drain and place in a large serving bowl.
For the sauce: In a small saucepan, warm the oil and salt over medium-high heat for 1 1/2 minutes. Remove the pan from the heat and stir in the basil. Let the mixture sit for 5 minutes to allow the flavors to blend.
Add the sauce and cheese to the gnocchi and gently toss until coated.