Start with the pasta. In a medium bowl, combine the flour and salt. Make a well in the middle of the flour, and add the egg. Begin to mix, adding the flour from the sides of the well a little bit at a time. The mixture should form a stiff dough. Add water as needed 1 tbsp at a time to form a soft and supple dough. Knead the dough for about 3-4 minutes. Let rest in the refrigerator, covered with plastic wrap for 30 minutes. With a pasta machine or by hand, roll dough out to desired thickness according to manufacturers instructions. Use a pasta machine on the fettuccine setting to cut the pasta into ribbons. Set cut pasta onto baking sheets dusted with flour, so they don’t stick together. Set aside until ready to use. Fill a large pot with water and bring to a boil. Once boiling, generously salt with sea salt.
While the water is coming to a boil, put a skillet over medium heat and melt the butter. When the foam subsides and the butter is a light golden color, add the sage. Cook for a few seconds, turning the sage leaves to coat, then remove from heat. Add the fresh pasta to the large pot of boiling water and cook for 1-2 minutes. Scoop the cooked pasta out of the pot and add it to the skillet with the butter and sage.
Quickly coat the pasta in the butter sauce, turning it over a few times to make sure it is evenly distributed. Take a little pasta water and add it to the pasta if necessary. Taste. Season with salt and pepper to taste. Scoop pasta into individual bowls and top with freshly grated Parmigiano Reggiano cheese.