Peel the cucumbers and cut into rounds 1-inch to 1 1/2-inches thick. Scoop out the middles to create a cup. This is most easily done with a melon baller; you could also use a knife to make the initial cut and then use a grapefruit spoon or dinner spoon to hollow out the walls.
Bring a pot of water to a simmer and cook the soba noodles according to package directions, usually 6 to 8 minutes. Drain and rinse the noodles under cool water. Transfer to a bowl.
Whisk together the rice vinegar, soy sauce, and sesame oil in a small bowl. Pour half the sauce over the noodles. Add the green onions to the noodles, saving a few for garnishing, and gently toss the noodles to coat them with the sauce. Soba noodles are fairly fragile, so your hands tend to be the best tool for this task.
Pack each cucumber cup with noodles, twirling them slightly to help them settle in the cup. Pour 1/4 teaspoon or so of the reserved sauce over the noodles in each cup and sprinkle the tops with a few green onions.
Serve right away or cover and chill for up to a few hours. If chilling, wait to add the reserved sauce until just before serving as the noodles tend to soak up the sauce.