For the marinade and sauce: Combine the garlic, ginger and scallion whites in a medium bowl along with the soy sauce, vinegar and chile-garlic sauce. Mix well to combine. Pour half the sauce into a shallow dish with the tuna steaks and let marinate for approximately 20 minutes, flipping halfway through. Reserve the remaining marinade separately to use as a sauce for the noodles.
For the noodles: Fill a large pasta pot with a perforated insert with heavily salted water and bring to a boil. (Alternatively, use a large pot with a small heatproof colander lowered into it.) Prepare an ice bath in a medium bowl and season with a pinch of salt; set aside.
Add the broccoli florets to the boiling water and cook until bright green, 1 to 2 minutes. Lift the insert and drain away excess water. Transfer the broccoli to the ice bath. Return the insert to the pot with the boiling water. Drain the broccoli and transfer to a small sheet pan or plate lined with paper towels.
Cook the noodles in boiling water until tender, stirring occasionally, 4 to 5 minutes. Remove the insert, draining the excess water, and pour the noodles into a large bowl. Dress the noodles with the reserved marinade. Add the carrots, broccoli and edamame and toss to combine.
For the cucumber salad: Mix together the fish sauce, vinegar, maple syrup, chile-garlic sauce and garlic in a small bowl. Toss with the cucumbers and set aside.
Toast the black and white sesame seeds in a dry skillet over medium heat until slightly fragrant, about 3 minutes. Remove the seeds to a bowl.
Wipe out the skillet with a paper towel. Increase the heat to medium-high and lightly coat with about 1 tablespoon canola oil. When the oil glistens, remove the pan from the heat and set the tuna steaks in the oil; you should hear a sizzle. (Reserve the tuna marinade.)
Return the pan to the heat and sear the tuna for about 30 seconds on each side. Turn off the burner and pour in about half the reserved tuna marinade, turning the steaks to coat. Return the pan to medium heat, bring the marinade to a simmer and cook for about 1 minute. Remove the steaks from the heat and let rest for a few minutes before slicing across the grain. Return the pan to low heat to keep the sauce warm
Add the soba noodle salad, cucumbers and sliced tuna to the bento box sections. Garnish the tuna and cucumbers with the toasted sesame seeds and the soba noodle salad with the scallion greens. Serve with the warm sauce.