Heat a large Dutch oven over medium-high heat. Add the avocado oil. Once hot, add the Italian chicken sausage and cook, breaking it into bite-sized pieces, until browned and cooked through, about 5-7 minutes.
Reduce the heat to medium. Add the onion to the same Dutch oven and cook for 4-5 minutes, stirring occasionally, until softened. Add the garlic and cook for another 30 seconds, until fragrant.
Add the tomato paste, Calabrian chili paste, Italian seasoning, smoked paprika, oregano, garlic powder, onion powder, red pepper flakes, cayenne, salt, and black pepper. Stir and cook for 1-2 minutes, allowing the tomato and chili pastes to caramelize slightly and the seasonings to become fragrant.
Pour in the chicken stock, stirring and scraping up any browned bits from the bottom of the Dutch oven.
Add the diced potatoes and bring the soup to a gentle boil. Reduce the heat to medium-low, cover, and simmer for 15-20 minutes, stirring occasionally, until the potatoes are fork-tender.
While the potatoes cook, make the roux. Melt the butter in a small saucepan over medium heat. Sprinkle in the flour and whisk continuously for 1-2 minutes, until completely incorporated and smooth.
Once the potatoes are tender, use the back of a wooden spoon or a potato masher to lightly mash some of the potatoes directly in the Dutch oven, leaving plenty of potato pieces whole for texture.
Keep the soup at a gentle simmer and slowly whisk in the roux until fully incorporated. Continue simmering for a few minutes, stirring frequently, until the soup begins to thicken.
Reduce the heat to low. Stir in the whole milk, heavy cream, and Parmesan cheese. Cook for another 3-5 minutes, stirring frequently, until the Parmesan has melted and the soup is creamy and warmed through. Avoid bringing the soup to a boil once the dairy has been added.
If the soup is thicker than you’d like, add additional milk a little at a time until it reaches your desired consistency. Taste and add more salt or pepper as needed.
Ladle into bowls and top with freshly grated Parmesan, red pepper flakes, sliced green onions, and a spoonful of sour cream.