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.
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