Frozen Pickled Onion and Horseradish Mignonette

Ingredients

• 1/2 cup Champagne or white wine vinegar
• 1/4 cup sugar
• 1 small red onion, thinly sliced
• 2 tablespoons freshly grated peeled horseradish or 1 tablespoon prepared horseradish
• 1/2 teaspoon kosher salt

Steps

1. Bring vinegar, sugar, and 1 cup water to a boil in a small saucepan, stirring to dissolve sugar. Add onion and cook until soft, about 5 minutes; drain onion.
2. Purée onion, horseradish, and 1/2 cup water in a blender until smooth. Strain through a fine-mesh sieve into a medium bowl, pressing on solids. Mix in salt.
3. Transfer mixture to a loaf pan and freeze 1 hour. Scrape mixture with a fork to break up frozen portions. Freeze, scraping and breaking up mixture every 30 minutes, until it resembles fluffy shaved ice, 2–4 hours.
4. DO AHEAD: Granita can be made 5 days ahead. Cover tightly with plastic wrap and keep frozen. Scrape before serving. (Serve alongside oysters.)