Attach the julienne blade to the mandoline and adjust it to the 1/8-inch-thick setting. Applying medium pressure, carefully run one of the cucumbers down the blade to form noodles, slicing until you reach the core. Rotate the cucumber a quarter turn and continue slicing and rotating until you've cut the entire cucumber. Repeat the slicing process with the second cucumber then transfer the cucumber noodles to a medium bowl.
Add the red onion, rice vinegar, water, sugar and crushed red pepper flakes (optional) to the bowl. Cover the bowl with plastic wrap and refrigerate the cucumber noodles for a minimum of 2 hours, stirring occasionally, until chilled.
When ready to serve, use tongs or a slotted spoon to transfer the noodles to serving plates and top with the sesame seeds.