Clean and dry a few coat hangers to dry the pasta on. Into the bowl of a food processor, add the flour, eggs, oil, and black pepper. Process until the mixture resembles breadcrumbs. Put the mixture onto your work surface and knead it lightly for a few minutes until it is smooth. It should be quite stiff. Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes. To make in a pasta machine: Take a quarter of the pasta and pat it into a flat rectangle with your hands. Feed it through the widest setting on the pasta machine. Fold that piece in thirds into a rectangle shape and feed it through again. After you have fed it through on the initial setting, there is no need to keep folding it, just keep feeding it through, making the setting narrower each time. If the pasta rips while using the pasta machine, don't worry, just fold it back into a rectangle and feed it through the widest setting again. A rip may mean that there is an obstruction in the pasta machine between the rollers. If that is the case, just open the machine to the widest setting and let whatever was stuck in there fall out. If the pasta sticks to the machine, just flour the machine a little to help ease the pasta through. When you have fed the pasta through on the narrowest setting, sprinkle the top with a little flour and fold it in half, short end to short end, then again, and again and again until you have a smaller rectangle. With the folded edge facing you, cut vertical strips about 1/2-inch wide along the width of the pasta, then carefully take one strip, unfold it completely and hang it on the coat hanger. Repeat with the rest of the pasta, using a quarter piece of the dough each time. To make the pasta by hand: Dust the work surface very lightly with flour. Take a quarter of the dough and put it on the work surface. Pat the dough with your hands into a flat rectangle. Lightly flour a rolling pin and roll it out until it is a very long and thin rectangle. My rectangle was 5 to 6 inches wide and very, very long. The pasta is ready when it is so thin that if you lift it up and put your hand behind it, you can see your hand through it. Sprinkle the top with a little flour and fold it in half, short end to short end, then again, and again and again until you have a smaller rectangle. With the folded edge facing you, cut vertical strips about 1/2-inch wide along the width of the pasta, then carefully take one strip, unfold it completely and hang it on the coat hanger. Repeat with the rest of the pasta, using a quarter piece of the dough each time. Once all of the pasta is hung, bring a large pan of salted water to the boil. Add the pasta, in one or two batches depending on how big your pan is, and cook for 4 to 5 minutes, or until the pasta is just cooked through. Using a pair of tongs, remove the pasta from the pan and, drain in a colander. If cooking the pasta in batches keep the first batch warm while cooking the rest. Once all the pasta is cooked and drained, drizzle with some of the olive oil, sprinkle a few basil leaves over the top and serve immediately. This is delicious used in the Creamy Pancetta Sauce with Mushrooms and Parmesan.