In a soup pot over medium-high heat, cook the Italian sausage until browned, about 10 minutes, breaking it up with a spoon as it cooks. Transfer the cooked sausage to a plate lined with paper towels, leaving the fat in the pot. If there’s more than about a tablespoon of fat, drain the excess.
Add the butter to the pot. Once melted, add the chopped onion and celery. Sauté for 4-5 minutes, scraping up any brown bits from the bottom of the pot.
Stir in the minced garlic and flour. Cook for about 2 minutes, stirring frequently to cook out the raw flour flavor.
Gradually whisk in the chicken broth until the flour is fully dissolved and the mixture is smooth.
Stir in the half-and-half, Worcestershire sauce, red pepper flakes (if using), diced potatoes, and the cooked sausage. Increase the heat to high and bring the soup to a boil.
Once boiling, reduce the heat to medium-low, so the soup is bubbling but not boiling aggressively. Cover the pot with the lid slightly ajar.
Let the soup simmer for about 15 minutes, or until the potatoes are tender and the soup has thickened to your liking. Stir occasionally to ensure nothing sticks to the bottom of the pot and the temperature is steady.
Taste and season with salt and pepper as needed.