Boil a pot of water over medium-high heat and cook the potatoes until tender, then drain and remove cooked potatoes to a large mixing bowl.
In a skillet over medium heat, heat 1 tbsp olive oil and sear the Kielbasa slices until browned and slightly crisp. Remove from the skillet and set aside for later.
Bring the heat down to medium and add the diced shallot to the leftover sausage grease in the skillet. Cook until the shallot softens.
Add the vinegar, olive oil, mustard, sugar, salt and pepper to a jar with a lid and shake until emulsified.
Pour the vinaigrette over the cooked sausage and shallot, add the cooked potatoes, and fold together. Simmer for a few minutes over low-medium heat to reduce, stirring occasionally.