In a large, deep skillet or Dutch oven, warm the olive oil over medium heat. Once hot, add the kielbasa slices and sauté for 4 to 5 minutes, turning occasionally until they develop a golden-brown exterior. Transfer the browned sausage to a plate and set aside.
Using the same pan, add the diced onion and cook for approximately 3 minutes until translucent. Stir in the minced garlic and cook for an additional 30 seconds, releasing its aroma.
Carefully pour in the chicken broth and heavy cream, then stir in the dry pasta. Season with paprika, salt, and pepper. Bring the mixture to a gentle boil, then reduce the heat to low, cover, and simmer for 12 to 14 minutes. Stir now and then to prevent sticking, and cook until the pasta is tender and most of the liquid has been absorbed.
Uncover the skillet, fold in the shredded cheddar cheese, and stir until the sauce becomes smooth and creamy. Return the reserved kielbasa to the skillet and continue cooking for 2 to 3 minutes, ensuring everything is heated through.
Finish by sprinkling with fresh parsley or green onions if desired, and serve immediately while hot.