In a large pot (I use a 6-¾ quart Dutch oven), combine water, wine, carrot, celery, onion, garlic, bay leaf, thyme, parsley, peppercorns, and kosher salt. Juice the lemon into the pot and then add the juiced halves.

Bring to a boil, then reduce heat and gently simmer for 20-25 minutes, uncovered. Adjust heat as needed to maintain a steady simmer.

Strain the broth through a colander or fine mesh sieve, discarding the solids, and return the clear broth to the pot.

Bring the strained court bouillon back to a boil. Remove the pot from heat, add the shrimp, stir to submerge them in the poaching liquid, and immediately cover the pot.

Let the shrimp cook in the residual heat based on their shell-on size. 3⅓5 count: 2 to 3 minutes, 26/30 count: 3 to 3-½ minutes, 2½5 count: 3-½ to 4 minutes, 16/20 count: 5 to 6 minutes, U/15 to U/12: 6 to 8 minutes. Cooking times are approximate and may vary by batch. (See note below about checking for doneness. If you find that they aren't fully cooked, replace the lid and check them in another 30-60 seconds.)

While the shrimp are poaching, prepare an ice bath by filling a large bowl ⅔ full with ice and cold water. Use a slotted spoon or strainer to remove the shrimp and transfer them to the ice bath. Let them cool for 10 minutes, stirring occasionally.

Once cooled, peel the shrimp and refrigerate until ready to serve. (Don’t leave them out at room temperature for more than 2 hours.) Store poached shrimp in an airtight container in the fridge for up to 3-4 days.