Prepare the salad: In a colander set over a large bowl, combine the cabbage, peppers, carrot, salt, and sugar. Toss to combine. Cover, and refrigerate overnight.
Make the dressing: Combine the dressing ingredients in a medium heatproof bowl set over a pan of simmering water. Cook, whisking constantly, until thick enough to coat the back of a spoon, about 10 minutes.
Remove salad from refrigerator, discard any liquid that has accumulated in the bottom of the bowl. Add the salad to the bowl. Add dressing and toss to combine.