Classic Shrimp Cocktail

Name: Classic Shrimp Cocktail
Ingredients: 2 pounds large shrimp (16-20 count), peel on; 2 large carrots, scrubbed but not peeled, cut into thirds; 1 stalk celery with leaves, cut into thirds; 4 sprigs thyme; ½ teaspoon whole peppercorns; 1 tablespoon kosher salt; 2 lemons; ¾ cup ketchup; 1 tablespoon fresh lemon juice; 1 to 3 tablespoons fresh horseradish or prepared horseradish; ½ teaspoon kosher salt; ½ teaspoon freshly ground black pepper; ½ teaspoon hot sauce, such as Tabasco (optional)