Place arugula, cucumbers, carrots, tomatoes, green onions in a large mixing bowl; set aside.
Bring medium pot to a boil and add salt. Cook soba noodles for 5-6 minutes or according to package instructions.
Drain and rinse noodles under cold running water to remove excess starch. Shake off excess water (or gently pat dry with paper towels), then toss noodles with sesame oil to keep them from sticking. Add the noodles to the bowl with vegetables.
Cut avocado in half, remove the pit, slice in a grid pattern, and scoop out the cubes. Add to the bowl.
Add mentsuyu, sesame seeds, and salt to taste. Toss everything together until well combined.
Divide salad into individual bowls or plates and top with soft-boiled egg halves, if desired. Serve immediately.