Melt the butter in a saucepan over medium heat. Add the potato and cook, stirring often, for about 5 minutes. Add the apple and continue cooking until the apples are tender, about 5 minutes more. Add the spinach and mix until the spinach has wilted. Season with salt and pepper. Transfer the mixture to a shallow bowl and set aside in the refrigerator until needed.
In the meantime, heat the oil in a second saucepan over medium heat. Add the onions and cook until soft, about 8 to 10 minutes. Transfer the mixture to a shallow bowl and set aside in the refrigerator until needed.
Roll the puff pastry to a size large enough to cover a 7.4" tart pan and leave some extra for folding in. Trim the excess dough. Fold the perimeter over to create a double thickness of dough at the sides of the tart pan.
Brush the base of the dough with the mustard. Spread the spinach mixture over the base and press down lightly. Cut the sausage into 3/8" thick slices. Arrange the slices in concentric circles on top of the spinach mixture. Strew the onions over the sausage and pat down lightly.
Bake the tart for 20 to 30 minutes until the pastry has puffed up and is a nice color.
Unmold the tart shortly after it is removed from the oven.