Classic Steakhouse Shrimp Cocktail

1. 1
   Fill a 4-quart pot with 6 cups of water.
2. 2
   Squeeze the lemon halves into the water and drop the peels into the pot.
3. 3
   Add the quartered onion, bay leaves, black peppercorns, and salt to the pot.
4. 4
   Bring the liquid to a rolling boil over high heat, then reduce heat to low and simmer for 10 minutes.⏱ 10 min
5. 5
   Prepare a large bowl filled with ice and cold water for chilling the cooked shrimp.
6. 6
   Remove the pot from heat and stir in the shrimp.
7. 7
   Cover the pot and let the shrimp poach gently off heat for 3 to 4 minutes until opaque and pink.⏱ 4 min
8. 8
   Transfer the shrimp immediately into the ice bath using a slotted spoon.
9. 9
   Whisk ketchup, horseradish, lemon juice, Worcestershire sauce, and hot sauce together in a small bowl.
10. 10
    Drain the chilled shrimp and pat completely dry with paper towels.
11. 11
    Arrange shrimp around the rim of chilled coupe glasses or on a platter with the sauce.
12. 12
    Bring water, white onion, bay leaf, and salt to a boil in a 3-quart saucepan over medium-high heat.
13. 13
    Add the shrimp, reduce heat to medium, and simmer for 2 minutes until just pink and firm.⏱ 2 min
14. 14
    Drain the shrimp and submerge them in an ice bath to halt cooking completely.
15. 15
    Drain well, pat dry, and cut shrimp into bite-sized 1/2-inch pieces.
16. 16
    Whisk the tomato clam juice, ketchup, fresh lime juice, and Mexican hot sauce in a large bowl.
17. 17
    Stir the chopped shrimp, diced cucumber, tomato, red onion, jalapeño, and cilantro into the sauce.
18. 18
    Season to taste with salt and chill in the refrigerator for at least 15 minutes.⏱ 15 min
19. 19
    Gently fold the diced avocado into the chilled mixture just before serving.
20. 20
    Ladle into chilled sundae or margarita glasses and serve with saltine crackers.