Make vinaigrette: Put shallots and vinegar in a bowl with 1/4 tsp. salt and let sit 20 minutes to 1 hour. Add 1/2 tsp. each salt and pepper; whisk in oil.
Put frisée, radicchio, persimmons, pomegranate, and walnuts in a large bowl. Toss with as much dressing as you like (you may have some left over) and add salt and pepper to taste.
*Find slightly sweet, complex French Banyuls vinegar, made from Grenache wine grapes and aged in oak, at igourmet.com ($16/500 ml.). Toast walnuts in a 350° oven until golden, 10 minutes.
Make ahead: The salad components, chilled separately up to 1 day.