Slice the seedless cucumber into thin rounds and place them in a clean container. In a saucepan, combine rice vinegar, salt, and sugar, then bring to a gentle simmer for about 3 minutes until dissolved. Remove from heat, stir in ice to cool, and pour over the cucumber. Seal and refrigerate for at least 4 hours.

In a medium saucepan, heat sesame oil over medium heat. Sauté grated garlic and grated ginger until fragrant, about 1-2 minutes. Add soy sauce, gochujang, brown sugar, honey, and rice vinegar. Simmer for 5 minutes, then mix cornstarch with water and stir into the sauce until thickened. Remove from heat and let cool.

In a small bowl, combine mayo, sriracha, sesame oil, and soy sauce. Whisk until smooth and set aside.

Preheat grill to medium-high heat. Season chicken thighs with Korean BBQ rub and drizzle of oil. Grill over direct heat for about 5-7 minutes per side until charred, then move to indirect heat and grill until the internal temperature reaches 165°F, approximately another 10-15 minutes. Coat the chicken in the BBQ sauce.

Cut open sandwich buns and spread the sriracha mayo on the cut sides. Layer grilled chicken and pickle slices on the bottom half of the bun, press the other half on top, and serve.