Cut the potatoes into quarters and put into a medium saucepan. Add enough water to cover and 1 teaspoon of the salt. Bring to a boil over medium-high heat and cook, uncovered, until just fork-tender, about 15 minutes. Drain.
Heat the oil in a large heavy skillet over medium-high heat. Add the andouille and cook, stirring often, until beginning to brown, about 2 minutes. Add the onions and cook, stirring often, until softened, about 3 minutes. Add the shallots and cook until beginning to soften, about 1 minute. Add the garlic and stir until fragrant, about 30 seconds. Add the cream andcook until reduced by half, 2 to 3 minutes. Stir in the mustard and mix well.
Add the potatoes, the remaining 1/2 teaspoon salt, and the pepper and cook, stirring, for 2 minutes.
Remove from the heat and serve, or cover to keep warm until ready to serve.
Yield: 4 servings