Take a 14-ounce package of smoked kielbasa and place it on a cutting board. With a sharp knife, slice the sausage in half lengthwise. Lay the sausage halves flat, then slice each one into ½-inch thick half-moon shapes. Set the pieces aside.
Set a large pot on the stove over medium heat. Once it’s warm, pour in 1 tablespoon of vegetable oil. Tilt the pot to evenly coat the bottom with the oil, then heat until the oil is hot and shimmering.
Once the oil is hot, add the kielbasa slices and 1 chopped medium yellow onion to the pot. Stir to combine, then cook until the sausage is lightly browned and the onions are tender, about 3 to 5 minutes.
Stir in 4 minced garlic cloves and cook until the garlic releases its aroma, about 1 minute. Pour in 6 cups of low-sodium chicken broth, stirring to blend, and make sure to scrape up any browned bits of onion or garlic from the bottom of the pot.
Stir in a 1.4-ounce package of dry vegetable soup mix, a 14.5-ounce can of black-eyed peas, a 14.5-ounce can of great northern beans, and a 27-ounce can of turnip greens. If desired, add 1 teaspoon of hot sauce and 1 teaspoon of Creole seasoning. Season with salt and freshly ground black pepper, mixing well to ensure all the ingredients are thoroughly combined.
Raise the heat to medium-high and bring the mixture to a boil. Once it starts boiling, lower the heat to a gentle simmer, cover the pot with a lid, and let the soup cook for 1 hour.
After an hour, take off the lid and set it aside. Give the soup a good stir, then taste it. Adjust the seasoning by adding more hot sauce, Creole seasoning, pepper, or salt to your liking, and stir well to blend everything. Once the flavor is just right, ladle the soup into bowls and serve it warm.