Preheat oven to 250ºF.
Place bagel chips on a large, rimmed baking sheet and warm them in the oven.
Heat a skillet over medium-high heat with the oil. Add beef and onions, and cook until crispy at edges and hot through. Add sauerkraut and sauté until warmed through, about 1-2 minutes.
Heat a saucepot over medium to medium-high heat. Melt butter and whisk in flour. Whisk in milk, season with salt and pepper, and thicken. Melt in cheese and stir in mustard.
In a bowl, stir together sour cream, ketchup and relish; season with salt and pepper.
Arrange warm chips on a serving platter. Top with meat and cheese sauce; drizzle with Russian dressing and top with lettuce, onions giardinera and chopped deli pickles.