Using a mandolin, slice unpeeled beets on the thinnest setting. Trim off edges with a paring knife. (Note: This method is less messy than peeling beets prior to slicing.)
Prepare cheese: Drain soaked nuts. In a food processor or high-speed blender, combine cashews, 1 tablespoon vinegar, lemon juice, melted coconut oil, water and garlic; process until smooth. Stir in chives, parsley and salt. Refrigerate cheese until ready to assemble recipe. Makes 1¾ cups vegan cheese.
Make dressing: In a food processor or blender, combine ¼ cup vinegar, herbs and shallot; blend until pureed. Continue to blend while adding oil in a thin, steady stream. Season with salt and pepper. Makes 1 cup of dressing.
To assemble carpaccio: Spoon 1 to 2 teaspoons of the vegan cheese in the center of half of the beet slices. Top with another beet slice. Place four beet sandwiches on a plate. Place a small pile of arugula on each plate and drizzle generously with herb dressing.