Heat a pot over medium heat. Once hot, add the oil. Saute the sausage to brown nicely. Add in the onion, garlic, and jalapeno and saute until softened.
Stir in the paprika, cumin, broth, and polenta. Bring to a low simmer (adjust the heat as needed) until the polenta is cooked, refer the instructions on the package for cooking time. Season with salt and pepper to taste. The consistency should be thick and creamy. Stir in more broth if needed to bring to the proper consistency.
Serve with chips. Garnish with tomato, cucumber, and cilantro. Drizzle with oil.