Grilled Shrimp Cocktail

INGREDIENTS

• 2 tablespoons freshly squeezed lemon juice
• 2 tablespoons granulated sugar
• 1/4 cup minced chives
• 4 garlic cloves, peeled, and grated on a Microplane grater
• 1/3 cup canola or vegetable oil
• 2 cups ketchup
• Twenty-four 8- to 12-count unpeeled shrimp (this means shrimp that come 8 to 12 to a pound)
• 2 lemons, each cut into 4 wedges
• 2 medium shallots, peeled, and grated on a Microplane grater
• Juice of 2 lemons
• 2 tablespoons freshly grated horseradish root (see Note)
• Freshly ground coarse black pepper
• 2 lemons
• 8 cups water
• 1/4 cup kosher salt
• 1/2 cup extra virgin olive oil
• 1 1/2 tablespoons Worcestershire sauce
• 1 tablespoon hot sauce
• Kosher salt
• 2 tablespoons high-quality bottled horseradish
• 3 cups ice