Put ¼ cup soy sauce and chicken thighs in a large bowl or storage bag (use up to ½ cup soy sauce, if needed); toss to coat. Let marinate for 15-30 minutes.
Preheat outdoor grill to a medium-high heat and clean grill grates.
Place the broccoli in a large bowl and toss with 1 tablespoon olive oil and a generous sprinkle of salt.
Remove the chicken from the soy sauce, allowing excess liquid to drip off. Season chicken with salt and pepper. Place directly on the hot grill grates and let cook for 2-4 minutes. Flip chicken and place the prepped broccoli on the grill on a grill pan or large piece of aluminum foil sprayed with nonstick cooking spray. Let the chicken cook for another 2-4 minutes or until the internal temperature reaches 162 degrees F. During the last 2 minutes of cook time for the chicken, brush on some teriyaki sauce. Toss the broccoli a few times during the cooking process and remove when cooked to your desired crispness. Remove all the chicken and broccoli when they are fully cooked.
Let the chicken rest on a plate or cutting board for 5-10 minutes, then cut into strips or bite-sized pieces.
Divide the rice, cucumbers, carrots, edamame, cabbage, avocado, green onion, chicken, and broccoli between bowls.
Enjoy the rice bowl with a drizzle of the remaining teriyaki sauce!
