On a rimmed baking sheet, toss the zucchini strips with the olive oil and salt. Grill the zucchini until just soft, about 45 seconds per side. Don't worry about the grill marks at this point. Remove to a board and lay out the strips.
Lay the strips of zucchini on a board. Roll 1 cube of cheese in 1 strip of ham, then position the ham and cheese roll on a zucchini strip so the exposed ends of the cheese will be rolled up in the zucchini, preventing it from squeezing out. Roll the zucchini around the ham and cheese roll. Use 2 skewers to secure the roll. Repeat with the remaining ingredients, placing 2 rolls on every pair of skewers. Place the skewers back on the grill and grill until just warmed through and grill marks have formed, about 1 minute per side. Serve warm.
Brie or Camembert make a good substitute if Robiola is unavailable.