Heat panini grill or George Foreman-style grill for 5 minutes. (Alternatively, lightly grease a nonstick pan with nonstick spray on medium heat and cover with a lid.)
In a bowl whisk together the vinegar and sugar until the sugar dissolves completely. Toss the cabbages and carrot in the bowl and set aside for 15 minutes then drain the liquid.
Spread the dressing on each slice of bread and top with cheese, layer with turkey and cabbage mixture, top with the other bread slice. Repeat for remaining sandwiches.
When the panini grill is hot (or the pan), cook the sandwich until the cheese is melted and the bread is golden brown. (If using a pan, cook on both sides until golden brown and the cheese is melted). Cut in half and serve with pickles and chips.