Coat roast with dry rub. Be sure to preheat grill, then grill roast at a high temperature. Cook until slightly rare and remove venison from heat. Brush butter onto one side of each slice of bread. Sprinkle cinnamon and sugar onto sliced apples and stir. Slice venison into thin pieces. Place a few venison slices on the unbuttered side of a slice of bread. Add a few apples and slices of cheese. Top with another slice of bread, butter side up. Place sandwiches on grill and cook on low heat. Place weight on the sandwiches using a Panini press. Flip sandwich once one side is toasted.