If cube steak is one large piece, cut in half lengthwise.
Prepare the marinade by mixing olive oil, vinegars, sugar and spices together in a bowl.
Pour marinade into a shallow dish and add steak, coating both sides.
Set aside while you prepare the grill or cover and refrigerate if grilling later.
Prepare a grill fire to 350° with hickory or oak for the best smoke flavor.
When you grill is just about ready, remove steak from marinade, reserving the marinade.
Place steak on a cutting board and sprinkle over diced vegetables. Roll up from the short side and secure with a toothpick.
Return steak rolls to marinade and spoon marinade over steak rolls.
Cook steak over an indirect fire with the grill lid closed about 8 -10 minutes.
Check internal temperature of steak in center of rolls and cook until desired doneness. We cooked ours to about 145° for medium in the middle and more done on the outside of the rolls.
Remove from grill and allow to rest about 5 minutes before slicing.
Slice into 1 1/2 inch pinwheels and serve immediately.