Coat a large wide pan with olive oil. Toss in the bacon, garlic and red pepper; bring to medium-high heat. When the garlic turns golden and is very aromatic, 2 to 3 minutes, remove it from the pan and ditch it -- it has fulfilled its garlic destiny. Add the cherry tomatoes to the pan and roll them around until coated. Add 1 cup of the stock, season with salt, reduce the heat to medium and let the tomatoes cook until they start to burst, 8 to 10 minutes.
Bring a large pot of well-salted water to a boil. Drop the pasta in the boiling water and cook for 2 to 3 minutes, or until it's tender but toothsome.
Drain the pasta and add it to the veggies along with about 1/2 cup reserved cooking water; toss vigorously to combine. Remove the pan from the heat, toss in the arugula, drizzle with the big fat finishing oil and sprinkle with Parmigiano. Serve immediately.
Put the all-purpose flour on a clean, dry work surface. Make a hole (this is also called a well) in the center of the flour pile that is about 8 inches wide (bigger is definitely better here). Crack all of the eggs and the yolk into the hole and add the olive oil, water and salt.
Using a fork, beat the eggs together with the olive oil, water and salt. Using the fork, begin to incorporate the flour into the egg mixture; be careful not to break the sides of the well or the egg mixture will run all over your board and you will have a big mess! Also, don't worry about the lumps. When enough flour has been incorporated into the egg mixture that it will not run all over the place when the sides of the well are broken, begin to use your hands to really get everything well combined. If the mixture is tight and dry, wet your hands and begin kneading with wet hands. When the mixture has really come together to a homogeneous mixture, THEN you can start kneading.
When kneading it is VERY important to put your body weight into it, get on top of the dough to really stretch it and not tear the dough. Using the heels of your palms, roll the dough to create a very smooooooth, supple dough. When done, the dough should look VERY smooth and feel almost velvety. Kneading will usually take from 8 to 10 minutes for an experienced kneader and 10 to 15 for an inexperienced kneader. Put your body weight into it, you need to knead! This is where the perfect, toothsome texture of your pasta is formed. Get in there and have fun!
When the pasta has been kneaded to the perfect consistency, wrap it in plastic and let rest for at least 1 hour. If using immediately do not refrigerate.
Roll and cut the pasta into desired shape. How smooth and supple!