Thinly slice the cucumber into rounds, about 1/8-inch thick.
Place cucumber slices in a colander and toss with 1/2 teaspoon salt. Let sit for 10 minutes to draw out excess moisture.
Rinse cucumber slices under cold water and pat completely dry with paper towels or a clean kitchen towel.
While cucumber drains, make the dressing: whisk together rice vinegar, sugar, sesame oil, and remaining 1/2 teaspoon salt until sugar dissolves completely.
Cut avocados in half, remove pits, and dice into 1/2-inch pieces.
In a large bowl, gently combine cucumber slices, avocado pieces, and dressing until evenly coated.
Sprinkle with toasted sesame seeds and let sit for 5-10 minutes to allow flavors to meld before serving.
