In a small bowl, whisk together mayonnaise, olive oil, onion and chopped onion. Let stand 2 minutes for extra flavor. Heat a lightly oiled skillet over medium-high heat. Pour in mayonnaise mixture and saute 10 minutes, stirring occasionally, until well mixed.
Stir in chopped onion, carrots and cabbage. Stir a few cubes of cheese into the mixture. Pour the put your sandwich patties into the skillet with mayonnaise mixture.
Remove patties from skillet and place in a medium bowl of dish that is lightly greased. Stir in poppy seed blueberry preserves or your favorite mustard, and pepper to taste. Serve sandwiches warm in a warm toast or in plastic sandwich bag.