Place the shrimp in a bowl with 1 cup of water, 2 cups of ice, and the sea salt, and refrigerate 30 minutes.
In another bowl, combine all the ingredients for the sauce and mix well. If you want, you can add some chili sauce to give a little kick to the sauce.
Place the sauce in the refrigerator until ready to serve.
Preheat your oven broiler and place a baking sheet in the oven.
Remove the shrimp from the water/salt brine. Rinse them under cold water, and pat dry using a towel or paper towels.
Toss the shrimp in a bowl with some olive oil.
Remove the baking sheet from the oven. It should be sizzling hot, so be careful!
Toss the shrimp on the baking sheet and place it back in the oven for just 2 or 3 minutes.
Turn the shrimp over and cook another 2 to 3 minutes.
Remove the shrimp from the oven and refrigerate until ready to serve.
Serve shrimp in a martini glass with the cocktail sauce or as desired.