Place beans in a large container and cover with several inches of cool water; let stand 8 hours to overnight. Drain and rinse.

Heat vegetable oil in a large pot over medium heat. Cook and stir sausage in hot oil until oils slightly release from sausage and edges brown, 5 to 7 minutes. Stir onion, celery, and poblano peppers into sausage; cook and stir until vegetables soften and start to turn translucent, 5 to 10 minutes. Stir garlic into sausage mixture; cook and stir until fragrant, about 1 minute.

Stir red beans, chicken broth, ham hock, bay leaves, black pepper, thyme, cayenne pepper, and hot sauce into the sausage mixture; bring to a boil, reduce heat to low, and simmer gently, stirring occasionally, for 1 1/2 hours. Add salt and continue simmering until beans are soft, meat is tender, and desired consistency is reached, 1 1/2 to 2 hours more. Season with salt.

Spoon rice into bowls, ladle red beans mixture over rice, and top with green onion.