Wash your hands. If needed, peel and de-vein the shrimp.
Heat 1 Tbsp. olive oil in a large saucepan over medium heat. Saute onions until soft and translucent - about 5 minutes.
Add tomatoes and artichokes and saute for 2 - 3 minutes, until the tomatoes begin to soften. Stir in wine and broth and boil for 5 minutes, reducing the liquid. Stir in 1 Tbsp. pesto and combine well. Add the spinach and cook until spinach is cooked down.
While vegetables are cooking and liquid is reducing bring pasta water to a boil. If using dried pasta, begin cooking. If using fresh pasta wait until the shrimp is cooked
Heat remaining Tbsp. of olive oil in a large frying pan over medium heat. Lay shrimp in 1 layer around the frying pan and cook until they begin turning pink and easily release from the pan. Turn them over and cook for another minute, until pink throughout. Remove immediately from the pan.
Once the pasta is finished, drain and place back in the pot. Stir in the remaining 2 Tbsp. pesto.
Divide pasta among 4 plates. Top each with ¼ of the vegetable mix and 5 - 6 shrimp.