Bring 2 quarts water to a boil in a Dutch oven. Add gnocchi to pan; cook 4 minutes or until done (gnocchi will rise to surface). Remove gnocchi with a slotted spoon; place in a large bowl. Add asparagus and shrimp to pan; cook 5 minutes or until shrimp are done. Drain. Add shrimp mixture to gnocchi.
Combine remaining 1 tablespoon water, basil, and next 4 ingredients (through garlic) in a food processor; process until smooth, scraping sides. Drizzle oil through food chute with food processor on; process until well blended. Add salt and basil mixture to shrimp mixture; toss to coat. Serve immediately.