Place potatoes in pot and cover with cold water; add kosher salt. Bring to a boil and then turn off heat. Let stand 20 minutes, covered. Remove potatoes from water and let stand until cool enough to handle. Slice into 1/8-inch thick slices. Heat skillet over medium-high; add canola oil and heat. Add sausages and fry until browned; remove to plate. Return pan to heat and add potato slices and onions. Fry with a pinch of salt and pepper for 5-6 minutes or until onions are translucent and potatoes are lightly browned. Cut sausages in half lengthwise and add to pan with the potatoes and onions.
Heat another skillet over medium heat, spread butter on one side of bread slices and place 4 slices, butter-side down, in skillet. Top each slice with 2 slices of Edam, 2 tablespoons of sauerkraut, 2 halves of sausage, a spoonful of potato/onion mixture, and 2 more slices of the Edam, in that order. Place a piece of bread on top of each, butter-side up. Grill sandwiches until bread is golden and cheese is melted, turning once during grilling. Serve with mustard on the side.