Thaw the shrimp and peel them, if necessary, tails on or off (your choice). Place them on paper towels and pat them dry, absorbing any excess moisture. Season them with salt, pepper, garlic powder, and paprika.
Cook the pasta:
Bring a large pot of water to a boil. Once boiling, add the spaghetti and boil according to the package directions. Reserve ½ to 1 cup of pasta water before draining the pasta. Transfer the pasta into a large serving or mixing bowl. The pot will be too hot and will dry the pasta.
Add the pesto to the pasta bowl and half of the reserved water and using kitchen tongs, combine the sauce and slowly add more pasta water until the pesto coats all of the spaghetti noodles and you like the consistency of the sauce. I typically use between ½ and ¾ cup total.
Cook the shrimp:
Heat a large pan over medium-high heat. Once hot, add a little oil and distribute it around the pan. Use kitchen tongs to place half of the shrimp on the pan, in a single layer, and cook them for 2 minutes per side, until they're opaque, have golden edges, and no longer pink.
Remove the shrimp from the pan onto the bowl containing the pesto pasta and repeat the process with the remaining half of the shrimp. Alternatively, you can serve the cooked shrimp directly on top of the pesto pasta.
Serve:
Serve the shrimp pesto pasta topped with Parmesan cheese.