In a bowl, combine the shrimp with salt, pepper, and ground paprika. Set aside.
Heat a large skillet over medium heat and add 1 tablespoon of olive oil. Once the oil is hot and sizzling, add the shrimp and cook for 1 minute per side, or until just pink. Transfer the shrimp to a plate and set aside.
In the same skillet, add 3 tablespoons of olive oil. Stir in the diced onions and sauté for a few minutes until translucent. Add the cherry tomatoes and garlic, and stir to combine. Cover the skillet and cook for 10–15 minutes, or until the tomatoes soften and begin to break down.
In the meantime, bring a pot of water to a boil. Add salt and cook the pasta according to package instructions. Do not overcook. Reserve 1 cup of pasta water, then drain the pasta and set aside.
Reduce the skillet heat to medium-low. Stir in the reserved pasta water and let it simmer. Add the arrabiata sauce and grated cheese, stirring until the sauce is well combined and slightly thickened.
Add the shrimp back into the skillet and let it warm in the sauce for 1 minute. Then toss in the pasta, making sure it’s evenly coated with the sauce.
Serve immediately, topped with extra grated cheese and fresh herbs, if desired.