To prepare pesto, bring a large saucepan filled with water to a boil. Add spinach and basil; cook 20 seconds. Remove spinach mixture to a bowl filled with ice water (reserve water in pan); let stand 30 seconds. Drain and pat dry with paper towels.
Place parsley and next 7 ingredients (through garlic) in food processor; process until finely chopped. Add spinach mixture and 2 tablespoons oil; process to combine. Place 3/4 cup pesto in a small bowl; place plastic wrap directly on pesto. Reserve for Pesto Chicken with Blistered Tomatoes and Vegetable Soup au Pisto.
To prepare pasta, return water in pan to a boil. Add pasta; cook according to package directions, adding asparagus during last 5 minutes of cooking. Drain in a colander over a bowl, reserving 3/4 cup cooking liquid.
Heat 1 tablespoon oil and butter in a large skillet over medium-high until butter melts. Sprinkle shrimp with red pepper and 1/4 teaspoon black pepper. Add shrimp to pan; cook 1 to 2 minutes on each side or until done. Remove shrimp from pan.
Add pasta mixture and reserved 3/4 cup cooking liquid to pan; cook 1 minute. Stir in remaining 6 tablespoons pesto, shrimp, grape tomatoes, and 1/4 teaspoon salt. Divide pasta mixture evenly among 4 bowls.