For the dressing: In a blender, combine the vegetable oil, rice vinegar, doenjang, lemon juice, mirin, sesame oil, carrots, ginger, and salt and pepper to taste. Process until smooth. Pour the dressing into a small bowl and set aside.
For the salad: Submerge the kale in a large bowl of cold water and massage vigorously for about 3 minutes to break down the chewy fibers. Drain, dry well and transfer to a large bowl.
Add the carrots, peppers, onions and sunflower seeds to the kale and toss together. Drizzle 1/4 cup of the dressing over the salad and toss to coat, adding more dressing to taste.
Divide the salad among four to six plates. Cut the avocado into thin wedges and squeeze some lime juice over top, if desired. Arrange the wedges on the salads and serve immediately.