Heat avocado oil in a medium skillet over medium heat. Add chicken and cook and stir until browned and no longer pink at the center, about 5 minutes. Remove skillet from the heat; set aside.
Add sesame oil, garlic paste, ginger paste, gochujang paste, soy sauce, brown sugar, honey, and rice wine vinegar to a small saucepan. Cook over low heat, stirring frequently, until thickened and heated through, about 5 minutes.
Return the skillet with chicken back to low heat. Add sauce to chicken and stir, cooking through until warm. Meanwhile, stir Sriracha and mayonnaise together in a small bowl.
To assemble, lay the buns on a plate. Cover each bun with lettuce, and drizzle with Sriracha mayonnaise. Spoon chicken over lettuce, add pickle slices, sprinkle with green onion, and drizzle with more Sriracha mayonnaise.
