How to Make It
Preheat oven to 375°.
Wrap beets in foil. Bake at 375° for 1 hour and 20 minutes or until tender. Remove beets from oven; remove foil. Cool.
Remove skin from cooled beets; cut beets in half. Combine beets, buttermilk, 1/2 cup sugar, half-and-half, juice, and 1/8 teaspoon salt in a blender. Scrape seeds from vanilla bean into blender; discard pod. Process mixture 2 minutes or until smooth. Pour into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Transfer to an airtight container; freeze.
Coat a jelly-roll pan with cooking spray. Place remaining 1/2 cup sugar in a saucepan over medium-high heat, stirring constantly with a silicone spatula. Cook 5 minutes or until sugar is completely melted and an amber color, stirring constantly. Remove from heat; immediately stir in nuts and remaining 1/4 teaspoon salt. Spread on prepared pan; cool 7 minutes. Break brittle into pieces; combine with oil in a food processor. Pulse until mixture is coarsely ground. Sprinkle hazelnut mixture evenly over sherbet.