Put in a jar all the vinaigrette ingredients. Mix well, taste and adjust seasoning if necessary.
In a salad bowl add the brussels sprouts, the apples, and the pomegranate seeds. With a spoon, slowly drizzle the vinaigrette on top. Do not add all the dressing; a few drops go a long way.
Serve immediately.
Notes
If you are preparing the salad ahead of time, add some lemon juice to the apple to prevent it from browning.