Make the pasta: On a clean wooden board or work surface, mound the flour and make a well in the center. Add the eggs and using a fork, gradually fold the flour into the eggs until shaggy. Begin to knead until a dough forms, then form into a ball and wrap in plastic. Refrigerate for at least 1 hour.
Meanwhile, make the chile-garlic oil: In a small saucepan, heat the olive oil over medium heat. Add the garlic and cook until lightly golden, 5 minutes. Add the chile flakes, reduce the heat to low and cook until golden brown, 1 to 2 minutes. Remove from the heat and add the salt and cherry tomatoes; let sit for 5 minutes. Transfer to a blender and purée until smooth.
Make the sauce: In a medium bowl, combine all the sauce ingredients and stir to combine.
Roll out the pasta: Cut the dough into 2 pieces and, using a rolling pin, roll 1 piece into an oval. Using a pasta machine, roll the dough out starting at the widest setting and ending with the fourth-thinnest setting (#5). Repeat with the other piece of dough, then dust both with flour and dry on a work surface for 15 minutes.
Cut each piece of dough in half widthwise and cut into spaghetti using the proper attachment for your pasta machine or stand mixer. Mound the pasta on a plate and refrigerate until ready to use.
Make the arrabbiata: Bring a large pot of salted water to a boil. Add the pasta and cook for 30 seconds, then drain and rinse with cold water.
In a wok, heat 2 tablespoons of vegetable oil over medium-high heat. Add the shrimp and season with salt. Cook until pink with charred spots, 1 minute. Transfer to a plate and add the remaining 2 tablespoons of oil to the wok. Add the pasta and stir-fry the noodles for 20 to 30 seconds.
Add the sauce along the outer ring of the wok and toss the pasta to coat. Add the reserved shrimp and the stock, and cook for 1 minute more, tossing constantly. Divide between bowls and garnish with parsley. Then drizzle with more chile-garlic oil and serve.