Heat the oil in a Dutch oven over medium-high heat. Add the andouille and cook for 4–5 minutes, stirring occasionally, until browned and some fat has rendered.
Add the onion, celery, and bell pepper to the pot. Cook for 5–6 minutes, stirring occasionally, until softened.
Stir in the garlic, Cajun seasoning, smoked paprika, and bay leaf. Cook for 30 seconds until fragrant.
Pour in both cans of red beans with their liquid, along with the chicken broth. Stir and bring to a gentle simmer.
Simmer uncovered for 20 minutes, stirring occasionally. Around the 15-minute mark, mash about a quarter of the beans against the side of the pot with a wooden spoon.
Remove the bay leaf. Taste and adjust seasoning with more Cajun seasoning or hot sauce as needed. Stir in half the green onions.
Serve over warm white rice, garnished with the remaining green onions and extra hot sauce at the table.