Fill a medium saucepan two-thirds full with water. Add celery, kosher salt, thyme, parsley, black peppercorns, and bay leaf. Bring to a boil, then reduce heat and simmer for 10 minutes to infuse flavors.

While the liquid simmers, gently remove the shells from the jumbo shrimp, leaving the tails intact. Rinse the shrimp under cold water to ensure they are clean and ready for poaching.

Carefully add the prepared shrimp and half of the lemon, cut in half, into the simmering water. Immediately remove the pot from heat, cover it, and let it sit for 3-4 minutes until the shrimp turn pink and firm.

Transfer the shrimp to an ice water bath using a slotted spoon. Allow them to sit for 2-3 minutes until completely cooled.

Once chilled, serve your shrimp with lemon wedges and a side of cocktail sauce for dipping.