Quickly marinate the chicken. Tenderize your chicken with a mallet in a bag (optional). In a medium bowl, whisk together the soy sauce, sesame oil, brown sugar, grated ginger, minced garlic, keep 1/4 cup of this sauce to the side for serving! Add the rest of it to a bowl, add the chicken and toss to coat. Cover and refrigerate for at least 10 minutes, or up to 6 hours.
Meanwhile, prepare the pickled cucumber salad. In a medium bowl, combine the rice vinegar, sugar, and salt. Stir until the sugar dissolves. Add the diced cucumber, shredded carrots, and thawed edamame. Toss well and refrigerate while preparing the chicken.
Mix the crispy chicken coating together and prep the chicken. Preheat the oven to 375ºF. In a shallow bowl, combine the panko breadcrumbs, sesame seeds, and garlic powder. Remove the chicken from the marinade, allowing the excess liquid to drip off. Press each cutlet firmly into the panko mixture, coating both sides evenly. Gently press the breadcrumbs into the chicken to help them adhere.
Sear the chicken in an oven safe skillet. Heat 2–3 tablespoons of neutral cooking oil in a large, oven-safe skillet over medium heat. Once the oil is hot, add the breaded chicken cutlets in a single layer. Sear for approximately 3 minutes per side, just until the coating turns lightly golden and crispy. Avoid cooking over high heat, as the sesame seeds and panko can burn quickly.
Bake the chicken. Transfer the oven-safe skillet directly to the preheated oven. Bake for approximately 12-18 minutes, depending on the thickness of the chicken, or until the internal temperature reaches 165ºF. This method allows the chicken to finish cooking without over browning the crispy coating. Transfer the chicken to a cutting board and let it rest for 3–5 minutes before slicing.
Make the spicy mayo. In a small bowl, whisk together the mayonnaise and sriracha until smooth and creamy. Adjust the sriracha to your preferred spice level. Refrigerate until ready to serve.
Assemble the chicken katsu bowls. Divide the warm cooked rice among four serving bowls. Top with sliced crispy chicken katsu, a generous scoop of pickled cucumber salad, and fresh avocado slices. Drizzle with spicy mayo and that soy sauce mixture you reserved and garnish with additional green onions or sesame seeds, if desired. Serve immediately while the chicken is warm and crispy.