For the pasta: mound flour on a work surface, make a well in the centre and add eggs, olive oil and water. Using a fork, beat the eggs lightly and with your fingers begin incorporating the flour into the egg mixture to form a dough. If the mixture is too dry, add 1 tbsp. of water at a time, as needed. The dough should not be sticky. Knead until you have a smooth dough. Shape into a disk and cover with plastic wrap. Place in the fridge for 30 minutes.
Cut the dough into 4 pieces and keep the pieces you are not working with covered in plastic wrap. Flatten a piece of dough with the palms of your hands and run through the pasta roller set at the widest setting. Fold the dough over and pass it once again at the widest setting. Continue rolling out the dough until you have reached the second-to-last setting. As the sheets of dough become longer and more difficult to handle, simply cut them in half. Cover the rolled sheets of dough with a dish towel and continue with the remaining dough.
Place the tagliatelle/spaghetti attachment onto the pasta roller. Roll the sheets of dough through the tagliatelle cutter. Place the tagliatelle on a parchment paper covered baking sheet, cover with a dish towel when done and place in the refrigerator until ready to boil.
Bring a large pot with water to a boil. Add salt and cook pasta 2-3 minutes. While the pasta is boiling, in a large skillet (large enough to hold the cooked pasta) heat the oil, add the garlic, parsley and red pepper flakes and sauté for 2 minutes. Stir in the paprika. Add the cooked pasta, toss to cover with the sauce.
Serve immediately with grated Parmigiano or ricotta salata.