Ingredients

• 1/2 cup coarse-grained mustard
• 1/4 cup water
• 1/2 cup heavy cream
• 1/4 cup olive oil
• 4 teaspoons sugar
• 1/2 cup chopped fresh dill
• 1/4 cup white wine, Champagne, or aged Sherry wine vinegar
• 2 teaspoons Dijon mustard
• 1 teaspoon kosher salt
• Freshly ground black pepper
• 2/3 to 3/4 cups extra-virgin olive oil
• 2 cloves garlic, minced
• 2 shallots, minced
• 4 (1/4-inch thick) chicken cutlets (1 1/2 pounds total)
• 1 to 2 tablespoons olive oil
• Salt and freshly ground black pepper

Instructions

1. In a bowl, combine well all sauce ingredients and season with pepper. Sauce may be made 1 day ahead and kept chilled, covered. Let sauce come to room temperature and whisk before serving.
2. In a small mixing bowl, whisk together the vinegar, mustard, salt, and pepper. Gradually whisk in enough oil to make a smooth dressing with a balanced taste. Stir in garlic and shallots. Place the cutlets in a glass pan, pour the marinade over, cover, and refrigerate for 2 to 4 hours.
3. Remove the chicken from the marinade (discard the marinade). Pat the chicken dry and season with salt and pepper. Grill chicken on an oiled rack set over glowing coals 1 to 2 minutes on each side, or until just cooked through.
4. Serve chicken with sauce.