Brown the Sausage: Heat the rich olive oil in a massive soup pot or Dutch oven over medium-high heat. Add the sliced sausage and cook, stirring occasionally, until the edges are aggressively browned and violently crispy, then transfer the meat to a clean plate.
Soften the Aromatics: Drop the heavy butter, chopped onion, carrots, and celery directly into the hot, greasy pot. Sauté the raw vegetables aggressively for 5 to 7 minutes until they turn completely soft and wonderfully translucent.
Build the Savory Roux: Stir the minced garlic, sweet paprika, Italian seasoning, dry mustard powder, and raw flour directly into the soft vegetables. Cook this dry mixture for exactly one minute, stirring nearly constantly to aggressively toast the flour.
Simmer the Heavy Broth: Pour in the savory chicken broth, vigorously scraping up the deeply browned bits from the bottom of the pot. Add the cold cream, diced potatoes, sweet corn, and the crispy sausage rounds straight into the liquid.
Boil and Thicken: Increase the heat to high to bring the soup to a violent, rolling boil, then immediately reduce the heat to a rapid simmer. Cook with the lid slightly open for exactly 20 minutes until the thick potatoes are wildly tender and crumbling.
Season and Serve: Physically remove the heavy pot entirely from the hot stove. Stir in the sharp apple cider vinegar, violently season the heavy soup with seasoning salt and black pepper to taste, and serve steaming hot!