Heat the vegetable oil in a large pot over medium heat. Add the smoked sausage and cook until browned.
Add the butter to the pot. Once melted, add the chopped onion, carrots, celery, and green pepper. Cook for 10 minutes, or until the onions become translucent and the carrots have softened.
Add the salt, pepper, and minced garlic. Cook for an additional minute until the garlic becomes fragrant.
Sprinkle the flour over the cooked vegetables and stir. Cook for a minute or two to remove the raw flour taste, then add the chicken broth, milk, and Worcestershire sauce. Stir to combine well. Increase the heat to a boil, then reduce to a simmer.
Add the smoked sausage and drained and rinsed beans to the pot and stir to combine. Continue to simmer, stirring occasionally, until it has thickened, about 20-25 minutes.
Remove from the heat and serve. Optionally, top with some chopped parsley and enjoy!