In a large bowl, combine mashed potatoes, egg yolks, salt and pepper. Mix until well combined. Place on a floured surface and knead until dough forms a ball.
Form a 1 inch by 1 inch ball and place on a floured bamboo mat with the lines going vertical. Gently press down and roll another mat on top horizontally to make the signature grooves on each ball of dough. Repeat with remaining dough.
Bring a large pot of salted water to a boil. Add gnocchi and cook for 3 to 4 minutes or until gnocchi have risen to the top; drain.
In a light-colored saucepan set over low-medium heat, melt butter. Continually swirl butter in the pan for about 2 to 3 minutes until butter turns brown, then add sage. Add gnocchi and toss the pan for about 4 minutes, until golden brown on all sides. Plate and sprinkle with Parmesan cheese.