Bring a large pot of well-salted water to a boil over medium heat.
Coat a large, wide pot set over medium-high heat with olive oil. Toss in the garlic and crushed red pepper. When the garlic becomes golden and very aromatic, remove from the pan and discard. Toss in the tomatoes, zucchini and onions and roll them around in the oil. Add 1 cup of the stock and season with salt. Reduce the heat to medium and cook until the tomatoes start to burst and give off their juices, 8 to 10 minutes. Add 1/2 cup more stock if the liquid level is very low.
Drop the tagliatelle into the boiling water and cook for 2 to 3 minutes. Toss the shrimp into the pot with the tomatoes and stir to combine. Drain the pasta, reserving 1/2 cup of the pasta cooking water, and then toss the pasta immediately into the pot with the tomato mixture. Add in the reserved cooking water, if needed. Toss vigorously to combine. Remove from the heat and drizzle some finishing oil over the top, then add the Parmesan and a sprinkling of fresh oregano to garnish. Transfer to a serving bowl or platter and serve immediately.
All-Purpose Pasta Dough:
Place the flour on a clean dry work surface. Make a hole (this is also called a well) in the center of the flour 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, a pinch of salt and 1 to 2 tablespoons water.
Using a fork, beat the eggs together with the olive oil, water and salt. Then 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 as 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, but not to 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 8 to 10 minutes for an experienced kneader and 10 to 15 minutes 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.
To roll out the pasta, you need to run the dough through a pasta roller a bunch of times to get it long and thin. To start, cut off about a quarter of the dough, keeping the rest wrapped up so it doesn't dry out. Squish the dough to flatten it. Run the dough through the pasta roller starting on the widest setting, number 1. Then dust the dough with flour, fold it into thirds, and put the dough through this setting two more times. If the dough ever feels sticky or tacky, dust with flour. Now adjust the setting to number 2 and repeat the process again, changing the setting each time until the dough reaches the desired thickness. Once the dough is rolled out, be sure to keep the pasta covered so it doesn't dry out. Repeat this process with the remaining dough, then cut the dough to the desires pasta shape.