Heat a large pan over medium-high heat. Season both sides of the chicken with salt and pepper.
Lightly coat the pan with avocado oil, then add the chicken. Cook for 5-7 minutes per side, or until fully cooked. Transfer to a cutting board, let it rest for a few minutes, then cut it into bite-sized pieces.
While the chicken cooks, prepare the brown rice according to the package directions.
Add all of the dressing ingredients to a blender and blend on high until smooth and creamy, about 1 minute.
In a small bowl, stir together the mayo and sriracha to make the sriracha aioli.
Warm the black beans in a small saucepan or in the microwave until heated through.
Divide the cooked rice between bowls, then top with the chicken, chopped cabbage, black beans, avocado, green onions, and jalapeños. Finish with fresh cilantro, a drizzle of the Asian dressing, and a dollop of the sriracha aioli before serving.