Make the peanut-ginger sauce by combining peanut butter, 1/3 cup tamari or soy sauce, 1/4 cup toasted sesame oil, 1/4 cup pickled ginger juice, 1 tablespoon gochujang, 1 tablespoon honey, 3 tablespoons lime juice, and the additional 1 tablespoon tamari/soy sauce listed for the sauce; blend or whisk until smooth and thin with water as needed.
Pat the sliced chicken dry and toss with 2 tablespoons toasted sesame oil, 1 tablespoon chopped fresh ginger, and chopped scallions.
Heat a large skillet over medium-high heat. Add the chicken mixture and cook, stirring occasionally, until the edges are browned and cooked through, about 5 minutes.
Add 3 tablespoons salted butter, 1 tablespoon tamari/soy sauce (as listed for cooking), and 4 chopped garlic cloves to the skillet; cook for about 1 minute more until fragrant and the butter melts, then remove the chicken from the skillet and keep warm.
In a bowl, combine the chopped mango, 1 tablespoon chopped pickled sushi ginger, lime zest and the 2 tablespoons lime juice noted with the lime zest, chopped cilantro, and chopped basil; season with a pinch of salt and toss to combine.
Divide cooked rice among bowls, top with the cooked chicken, spoon over peanut-ginger sauce, add the mango-herb salsa, and finish with sliced avocado; serve extra sauce on the side.
