Take out a platter for the bites, and toothpicks. Set both aside but in easy reach.
Cut the cucumber ribbons by placing a cucumber on a cutting board and using a vegetable peeler to slice thin pieces off the cucumber, length-wise. Start at one end and go all the way to the other end of the cucumber. Keep making thin slices of cucumber until you start to see the seeds. Then flip the cucumber over (so the flat part is facing down on the cutting board) and do the same on the other side. Do the same to the other two sides.
As you’re slicing the ribbons, place them on a paper-towel lined plate in a single layer to absorb any excess moisture out of the cucumber. When you run out of space, add more layers of paper towels.
While the cucumber is on the paper towels, slice cherry tomatoes on a cutting board with a sharp knife. Once done, set aside.
Start assembling the bites, beginning with the prosciutto. Take one large piece of prosciutto and pull it apart into two long piece. Take one of those pieces and start to roll it together (in a flat piece) into roughly a one inch sized piece. Once all the way rolled up, set it aside.
Take one slice of cucumber and fold it back and forth onto itself into roughly that same one inch sized piece. You will likely need to do this with two hands so the cucumber folds don’t slip out.
Assemble the bites by taking the prosiutto, laying the cucumber ribbon on top of it, then place half a tomato on top of the cucumber. Take a toothpick and carefully pierce all three ingredients starting with the tomato. Be sure to put the toothpick all the way through the prosciutto - this will prevent the prosciutto from slipping off the toothpick.
Place the bite on the platter and repeat the assembly process until all of the bites are put together.
Once all the the bites are assembled on the platter, drizzle balsamic vinegar on top of them, making sure to get a little on each bite (about a quarter of a cup total, or more if needed). Serve immediately.