Put the wine in a pot over medium heat. Bring to a simmer. Cook until the liquid is reduced to about 1/2 cup. It will be thicker and deeper in color. Set aside to cool.
Mix the flour and salt together. Whisk the eggs in a bowl.
Mound the flour on a clean, non porous surface (Cutting board, marble, stainless steel, granite, butcher block, etc.). Create a "bowl" in the middle to mix in the ingredients.
Pour the eggs into the indentation in the flour. Add in the wine and oil. Fold the flour into the wet ingredients. Be careful that they don't spill out. Continue folding in until a dough begins to form. Flour the surface, as needed, to continue kneading.
As the dough forms, continue kneading it with the palm of your hand. Fold it, and knead some more. Do this for about 5 to 10 minutes. Then form the dough into a ball and cover it. Let the ball rest for about 5 minutes.
Split the ball into 4 pieces. Roll them into balls. Flatten the balls by hand or with a rolling pin. Then put through a pasta machine. Start on the widest setting. Roll it into a long thin strip. Fold the dough in 1/2 and roll through again to get even strips. Then, roll again at the next lowest setting. Repeat this process until it is the desired thickness. If the pieces are too long, cut them to a manageable size.
Once the sheets are at the desired thickness, use the cutter attachment of the pasta machine to cut into strips.
Boil water with salt. Cook the pasta for about 2 minutes. Toss with your favorite sauces and toppings. Mangia!