Melt 1 tablespoon butter in a small saucepan; add green onion bottoms and sauté until softened. Add shrimp and green onion tops (reserve a few for garnish) and sauté until shrimp are pink and just cooked through; set aside.

Place chicken broth in a saucepan over medium heat; bring to a low simmer, reduce heat, and keep hot.

Place 1 tablespoon butter and olive oil in a wide heavy pan; place over medium heat. Add minced onion and cook, stirring, until onions are translucent, about 10 minutes; do not brown. Add Arborio rice and cook, stirring constantly, for 3 to 4 minutes; rice will begin to become translucent. Quickly add ½ cup hot broth, stirring constantly until liquid is completely evaporated. Repeat process, ½ cup broth at a time, for about 20 minutes or until all liquid is incorporated and rice is just cooked through; it will be firm, but not crunchy in the center. (If you need more liquid, use very hot water.)

Stir in the reserved shrimp mixture, remaining 2 tablespoons butter, cheese, and crabmeat; remove from heat when cheese melts. Taste and add salt if desired.Serve hot, garnish with green onions if desired.