Bring a large pot of salted water to a boil over high. Meanwhile, place spinach in a large colander. Add pasta to boiling water; cook according to package directions for al dente. Reserve 1 1/2 cups cooking liquid; drain pasta in colander over spinach (to wilt spinach).

While pasta cooks, heat 2 tablespoons oil in a large skillet over medium-high. Add artichokes to skillet; cook until browned, 2 to 3 minutes per side. Slide a thin metal spatula under artichokes if they stick. Place artichokes in a medium bowl.

Heat remaining 1 tablespoon oil in skillet over medium-high. Sprinkle shrimp with 1/4 teaspoon salt, and add to skillet; cook until opaque and just cooked through, about 3 minutes, turning once or twice. Transfer shrimp to bowl with artichokes.

Reduce heat to medium. Add 1 cup reserved cooking liquid to skillet; bring to a simmer, scraping bottom of skillet using a wooden spoon to release browned bits. Add cheese and remaining 1/4 teaspoon salt, stirring until cheese is mostly melted, about 2 minutes. Stir in pasta and spinach until well coated, adding remaining 1/2 cup cooking water, about 1/4 cup at a time, as needed to lightly coat pasta. Gently stir in reserved shrimp and artichokes. Sprinkle with pepper. Serve immediately.