Step 1: Brown the sausage
In a large soup pot or Dutch oven, heat olive oil over medium heat. Add sausage and cook, breaking it apart with a spoon, until browned and cooked through. Drain excess grease if necessary.

Step 2: Add aromatics
Add chopped onion, garlic, carrots, and celery to the pot. Sauté for 5–6 minutes, until vegetables soften and onion is translucent.

Step 3: Add potatoes and broth
Stir in the diced potatoes and chicken broth. Bring to a boil, then reduce heat and simmer uncovered for 15–20 minutes, or until potatoes are fork-tender.

Step 4: Make it creamy
Once the potatoes are cooked, stir in the milk (or half-and-half) and shredded cheddar cheese. Simmer gently for 5 more minutes, stirring until the cheese melts into the soup.

Step 5: Season and serve
Taste and adjust seasoning with salt, pepper, and crushed red pepper if using. Garnish with chopped parsley or extra cheese before serving.