Add the chicken thighs to a large resealable freezer bag.
In a medium bowl or large mason jar, combine the soy, sugar, honey, rice wine vinegar, vegetable oil, Asian chili sauce, lime juice, ginger, sesame oil, hot chili oil, pepper, scallion whites and garlic. Whisk or shake until the sugar has completely dissolved.
Add a third of the marinade to the bag with the chicken and toss to completely cover. Marinate for at least 2 hours and up to overnight. Refrigerate the remaining marinade in a jar, covered, until ready to cook.
Cook the soba noodles according to the package instructions. Rinse until cool, then set aside in a bowl.
Heat a grill pan or cast-iron pan over medium heat.
Remove the chicken from the marinade. (Discard any used marinade left in the freezer bag.) Cook the chicken, turning, until cooked through, 2 to 3 minutes a side. Remove to a cutting board and slice into strips.
Add the reserved jarred marinade to a medium pot over medium-high heat. Bring to a boil and remove from the heat. Pour half of the marinade over the noodles in the bowl and toss until completely coated and warmed through. Add the sliced peppers and toss.
Pile the noodles onto a platter, arrange the sliced chicken on top and garnish with the reserved scallion greens, cilantro and toasted sesame seeds. Serve the remaining hot marinade in a pitcher on the side.
To make ahead: This makes a great kit meal. Put the chicken in a large resealable freezer bag. Make the marinade and pour one-third over the chicken, seal the bag and coat. Save the remaining marinade in a mason jar and seal. Put the cooled rinsed noodles in a resealable freezer bag. Put the sliced peppers in a resealable freezer bag. Put the sesame seeds and scallions in tiny disposable containers with lids. Put the cilantro in a small resealable freezer bag. Put everything on a sheet pan and store in the fridge. When you are ready to cook, follow the instructions above.