Melt butter in a large stockpot and brown sausage.
Add onion and garlic and cook until onion is softened. If using flour to thicken, sprinkle it on the meat and onion now and stir well (see note for alternative).
Pour broth over ingredients in pot and stir well to incorporate the flour. Then add the potatoes, salt, basil, and pepper, cover and bring to a boil; turn heat to medium and cook about 15 minutes or until potatoes are tender.
Stir in corn and milk, bring to a simmer (just under a boil) over medium-high heat to heat and thicken.
Serve topped with chopped parsley or chives.
Notes
*For a gluten-free thickener, add 1 1/2 tablespoons cornstarch or arrowroot powder, but stir it into the cold milk right before adding at the end of the recipe. Cook enough to thicken.