Combine the salt, sugar, and water in a mixing bowl, stirring to dissolve — yes, you’re making a brine. Add the ice and set aside while prepping the shrimp.
Use a pair of kitchen scissors to remove the veins from the shrimp without removing the shell.
Put the shrimp in the brine and refrigerate for 20 to 25 minutes.
Meanwhile, make the cocktail sauce. Place almonds in the bowl of a food processor and pulse until pieces resemble course meal. Add all the other ingredients, except the salt, and pulse until desired consistency is reached. I like mine a little on the chunky side.
Let the sauce sit in the work bowl for 5 minutes, then taste. Add salt as desired. Refrigerate at least 3 hours before serving. It will keep for up to 1 week.
Place a half-sheet pan or foil-lined broiler pan about 8 inches under the broiler and heat for 5 minutes.
Remove the shrimp from the brine and rinse under cold water. Dry thoroughly on paper towels. Discard the brine and return the dry shrimp to the same bowl. Toss with oil and sprinkle with Old Bay seasoning.
Arrange the shrimp on the sizzling-hot sheet pan and slide back under the broiler. Set your timer for 2 minutes.
Clean out the bowl and stick it in the freezer.
Flip the shrimp quickly with tongs and return to the broiler for 1 minute.
Transfer the shrimp to the chilled bowl and toss a few times to knock down the heat. Place in the freezer, tossing every few minutes until the shrimp are thoroughly cooled, about 15 minutes.
Peel the shrimp and serve alongside the sauce.