Put the potatoes into a saucepan and add enough water to cover them. Add 1 t of the salt. Bring to a boil over med-high heat and cook for about 15 minutes or until the potatoes are fork-tender. Drain.
Heat the oil in a big heavy skillet over med-high heat. Add the andouille sausage and cook, stirring, for about 2-4 minutes or until getting browned. Add the onions and cook, stirring, for about 3 minutes or until softened. Add the shallots and cook, stirring, for about 1 minute. Add the garlic and cook for about 1 more minute, stirring. Add the cream and cook until it gets reduced by about half, 3-5 minutes. Stir in the mustard and mix it all up well.
Add the potatoes, the remaining 1/2 t of salt and the pepper. Cook, gently stirring, for about 2 minutes.
Remove the pot from the heat and serve (or cover to keep warm until serving time).