In a small saucepan, heat the rice vinegar, salt and sugar just until everything dissolves. Pour the liquid into a small bowl and add a handful of ice. Add the cucumbers and cabbage to the bowl and put them in the fridge for a couple hours to marinate.
In the same saucepan, combine the sesame oil, garlic, ginger, soy sauce, and gochujang, brown sugar, and rice vinegar. Cook on medium heat until simmering. Mix the cornstarch and water. Add to the sauce and whisk until smooth. Remove from heat.
Combine the mayo, sriracha, sesame oil, and soy sauce. Mix well. Set aside.
Preheat the grill to 450℉.
Rub the chicken with oil, then season with salt and pepper.
When the grill is ready, place the chicken on the grates and cook for 4 minutes per side. Then lower the heat to 375℉ and continue cooking, basting with the bbq sauce regularly on both sides, until the chicken reaches 165℉.
In the last few minutes of cooking, you can also heat the sandwich buns on the grill.
To assemble, coat both sides of the bun with sriracha mayo. Place a piece of chicken on and top with cucumbers and cabbage.