Peel shrimp, and devein, if desired. Set aside.
Bring 6 1/2 cups water and 1/2 teaspoon salt to a boil in a 3 1/2-quart saucepan. Add asparagus pieces, and cook 4 minutes. Remove asparagus with a slotted spoon, and set aside, reserving broth in pan over low heat to keep warm.
Sauté diced onion in hot oil in a large Dutch oven over medium heat 6 minutes or until tender and golden.
Add 1 1/2 cups rice, and cook, stirring constantly, 2 minutes. Reduce heat to medium; add 1 cup reserved hot asparagus broth. Cook, stirring constantly, until liquid is absorbed.
Repeat procedure with remaining hot broth, 1/2 cup at a time (cooking time is about 20 minutes). Add shrimp and asparagus pieces, and cook, stirring constantly, 3 minutes or just until shrimp turn pink. Remove from heat; stir in salt and pepper. Serve immediately.