Gribiche is a classic French sauce that traditionally combines hard boiled egg yolks with mustard and oil. The gribiche sauce for this salad includes vinegar, relish and capers to create a tangy and briny dressing for the shredded Brussels sprouts.
Whisk together 1 tablespoon each Dijon mustard and capers, 2 tablespoons white wine vinegar, 4 teaspoons sweet relish and 1/4 cup olive oil in a large bowl. Fold in 1/2 cup finely chopped parsley and 2 finely chopped hard-boiled eggs. Add 10 ounces shredded brussels sprouts (about 5 cups) and toss to fully coat. Season with salt and pepper; let stand 10 to 15 minutes at room temperature to soften slightly.