In a large skillet over medium-high heat, brown the sausage, stirring, about 6 minutes. Drain on paper towels.

In a large, heavy saucepan, combine the potatoes and 1 teaspoon of the salt. Cover with water by 1-inch and bring to a boil. Reduce the heat to medium-low and simmer until the potatoes are fork tender, about 25 minutes. Drain the potatoes and return them to the cooking pot. Add the cream, butter, the remaining 3/4 teaspoon salt, and black pepper to the potatoes. Place over medium-low heat and mash with a potato masher until no longer lumpy, about 2 minutes. Add the cooked andouille and continue mashing until light and fluffy, about 2 minutes.

Serve immediately.