In a sauté pan, melt the butter over medium heat and add the onions, peppers, and celery. Cook until the onions are transluscent, about 5 minutes. In a large mixing bowl, combine the cooked vegetables with the rest of the ingredients. Season to taste with salt and pepper. Refrigerate until ready to use.
To make the coleslaw, combine the mayonnaise, sugar, milk, buttermilk, lemon, and balsamic vinegar in a bowl. Season with salt and pepper to taste and mix until smooth. Add the cabbage, carrots, and onions to the mixture and toss well. Cover and refrigerate for at least 2 hours.
For the sandwich, place a ½ cup of the crab salad on the bottom of a slider bun. Top with ¼ cup of the coleslaw, a slice of Cheddar cheese, and the top 1/2 of the bun and serve with french fries and tartar sauce on the side.