In a large bowl, combine egg, 1/4 cup cola, crushed Saltines, 4 tablespoons salad dressing, Parmesan cheese, ground beef, salt and pepper. Mix until combined, but do not overmix. Mixture will be very moist.
Shape into 6 patties, cover with plastic wrap and refrigerate at least 20 to 30 minutes.
In a small bowl, combine remaining cola and salad dressing. Set aside.
Make sure grill grates are greased well. Heat grill to medium-high. When very hot, add patties.
Grill for 5 minutes, Brush with glaze and flip over. Brush other side with glaze. Continue to grill until desired degree of doneness. You can brush 1 more time with glaze if desired.
Serve on buns with desired toppings and condiments.