Pour olive oil into a 4–5 litre sauté pan and set over medium-high heat.
Add sliced kielbasa and diced onion, sautéing until the sausage is browned and onions are translucent.
Incorporate the minced garlic, stirring continuously, and cook for approximately 30 seconds until fragrant.
Add chicken broth, diced tomatoes with juice, milk or cream, dry pasta, salt, and black pepper. Stir well to combine.
Bring contents to a gentle simmer and cook uncovered for 15 minutes, stirring occasionally, until pasta is tender and sauce is slightly thickened.
Remove pan from heat. Stir in half of the shredded Cheddar cheese until evenly melted.
Scatter the remaining cheese over the surface, cover, and let stand until cheese is melted, lightly golden, and bubbly.
Sprinkle with thinly sliced scallions and serve hot.
