Combine first 8 ingredients in a small bowl; toss gently.
Let stand 30 minutes, tossing occasionally.
Cut a thin slice off top of each roll; discard slices. Set tops aside.
Cut a 2-inch-wide, V-shaped wedge down length of each roll. Reserve bread wedges for another use.
Drain vegetable mixture. Line each roll with a lettuce leaf; top evenly with ham and turkey. Spoon vegetable mixture evenly over meat; cover with bread tops.