In a large deep pan, heat the olive oil over medium-high heat until hot. Add the kielbasa and onion and cook, stirring occasionally, until the kielbasa begins browning, 2 to 3 minutes.
Add the mushrooms and squash (the pan will be quite full) and continue cooking, stirring occasionally, until the vegetables are tender and the kielbasa has browned, 3 to 5 minutes.
Add the chicken broth, diced tomatoes with their juices, milk, and pasta. Stir to combine and bring to a boil. Reduce the heat to low and simmer, stirring occasionally, until the pasta is fully cooked, 15 to 20 minutes. Make sure that the pasta is submerged in the liquid throughout simmering, so that it absorbs the broth and fully cooks.
Add the spinach and once it has wilted, after 1 to 2 minutes, add the Cheddar. Mix well for 1 to 2 minutes until the cheese is nice and melty and coating everything. Garnish with sliced green onions (if using) and enjoy!
Once cooled, store airtight in the refrigerator for up to 3 days. To reheat, warm in a pan over medium heat until heated through, or microwave.