Place onion slices on a grill over medium heat (using a grill basket will help keep pastrami from falling through the gates). Cook for 5 minutes per side or until lightly charred. Remove from the grill & toss with 2 Tbsp. dressing.
Meanwhile, lightly brush one side of each bread slice with the remaining dressing. Place on the grill while onions are cooking, the dressing side down, and place cheese on 4 of the bread slices. Top with onions & the pastrami and close the sandwich.
Reduce heat to low (or move sandwiches away from direct heat) & grill for about 5 min per side to lightly brown and heat the cheese & pastrami.