Heat the olive oil in a large pot over medium heat. Brown the sliced andouille, 4–5 minutes. Transfer to a plate.
Melt the butter in the same pot. Add onion, celery, and bell pepper. Cook until softened, about 6–8 minutes.
Stir in the garlic, Cajun seasoning, smoked paprika, and cayenne. Cook 30 seconds until fragrant.
Sprinkle in the flour and stir constantly for 1 minute to form a light roux.
Add the potatoes and pour in the chicken broth. Scrape up any browned bits. Bring to a boil.
Lower heat and simmer gently until potatoes are tender, 15–20 minutes.
Partially mash the soup with a potato masher to thicken, leaving some chunks for texture.
Stir in the cream, lemon juice, and the browned sausage. Simmer 2–3 minutes to heat through.
Season with salt and black pepper to taste. Ladle into bowls and garnish with scallions, parsley, and cheddar.