In a small bowl, combine the seasme oil, tamari, lime juice, honey, ginger, garlic, brown sugar, crushed red pepper flakes, and salt and pepper to taste. Whisk thoroughly to combine. Taste, and adjust seasoning as needed. Set aside.

Place the carrots and bok choy in a steamer basket and steam over simmering water for just 2 minutes. Remove from heat and rinse under cool running water. Drain well, then transfer to a large bowl. Add the chopped apples, and drizzle with the dressing. Toss to coat, then fold in the toasted almonds. Serve immediately.