Peel shrimp, reserving the shells. In a skillet over medium heat, cook the garlic and shrimp in 2 tablespoons of olive oil, stirring frequently to keep the garlic from browning. When shrimp are cooked through, remove from heat, cool and cut into 1/2-inch pieces.
Bring water to a boil in a Dutch oven over high heat. Add shrimp shells, boil for 5 minutes, then strain out shells and discard. Stir in the orzo and cook for 5 minutes. Stir in the asparagus pieces and continue cooking until the pasta is al dente, about 4 minutes. Drain into a mesh sieve, and rinse in cold water.
Toss pasta and asparagus with 2 tablespoons of olive oil, shrimp, and green onions until evenly coated. In a separate bowl, whisk the vinegar, lemon juice, mustard, and basil until incorporated. Pour over pasta mixture and toss well; season to taste with salt and pepper. Chill for 2 hours.
