Stir in the green onion, celery, and prosciutto; cover the pot and cook the mixture, stirring once, for 2 minutes.
Increase heat to medium-high. Stir the scallops and oysters with liquid into the green onion mixture; cook uncovered, stirring frequently, until the scallops are cooked through, about 5 minutes.
Stir the corn, tomato, half-and-half, jalapeno pepper, sesame oil, and cilantro into the oyster mixture.
Remove the pot from heat, cover, and allow the stew to sit until uniformly heated, about 10 minutes.