Heat 2 tablespoons of olive oil in a large pot or Dutch oven over medium heat. Add the sliced kielbasa and sauté for 4-5 minutes, stirring occasionally until browned and slightly crispy. Remove the kielbasa and set aside.

In the same pot, add the chopped onion, diced carrot, and chopped celery. Sauté for about 5 minutes, stirring often, until they are soft and fragrant.

Stir in the minced garlic and a pinch of red chili flakes, cooking for about 1 minute until fragrant. Be careful not to let the garlic burn.

Add the diced potatoes and chicken stock to the pot. Bring to a boil, then reduce the heat to low, cover, and simmer for 10-12 minutes, or until the potatoes are tender.

In a separate bowl, mix the whole milk with a ladleful of hot soup to temper it. Stir well, then return the tempered milk mixture back to the pot.

Add the browned kielbasa and shredded cheddar cheese to the pot, stirring gently until the cheese melts into the soup. Heat through for an additional 2-3 minutes.

Stir in the chopped parsley and season with salt and pepper. Let it simmer for another minute before serving.