This recipe adapted from Suzanne Goin's "Sunday Suppers at Lucques: Seasonal Recipes from the Market to Table" (Knopf, 2005).
Preheat oven to 375 degrees. Spread hazelnuts on a baking sheet; toast, stirring once, until fragrant and lightly browned, 8 to 10 minutes. Let cool; coarsely chop nuts, and toss with 1 teaspoon hazelnut oil and salt.
In a small bowl, combine chopped shallots, pomegranate juice, sherry and rice vinegars, and salt; let stand 5 minutes. Whisk in olive oil and remaining 1 tablespoon hazelnut oil.
In a large bowl, toss persimmons, sliced shallots, and pomegranate seeds with dressing; season with salt, pepper, and a squeeze of lemon. Gently toss with arugula. Arrange salad on a serving platter, and garnish with hazelnuts. Serve immediately.