Cook the pasta: Start a pot of well salted water to a boil. Boil the pasta until it is just al dente. Start tasting a few minutes before the package recommends: you want it to be tender but still a little firm on the inside; usually around 7 to 8 minutes. Just before draining, reserve 1 cup pasta water! Then drain the pasta.
Meanwhile, cook the shrimp: Pat the shrimp dry. In a medium bowl, mix the shrimp with spices. In a large skillet, heat the olive oil on medium high heat. Cook the shrimp for 1 to 2 minutes per side until opaque and cooked through, turning them with tongs. Remove from the heat and set aside.
Serve: Place the pasta in a bowl (not the pasta pot). Stir together the pasta, pesto, and 1/2 cup pasta water, tossing with tongs until the pesto is well distributed and the pasta water forms a creamy sauce. Add more pasta water if desired. Stir in 1/4 teaspoon kosher salt and taste. If the flavor doesn’t pop, add a few more pinches until it does. Top with the cooked shrimp and serve immediately. (Store any leftovers refrigerated: note that pesto can get gummy when reheated, so it’s best to eat leftovers cold or room temp.)