Make the Homemade Clamato Juice. Core and chop the tomatoes and run them through a juicer into a medium bowl. Alternatively, grate the tomatoes with a handheld grater over a sieve set over a medium bowl or 2-cup measuring cup. You will need 1 cup of tomato juice.
Add the remaining ingredients for the “Clamato Juice” (garlic through black pepper) to the tomato juice. Allow the juice to marry with the other flavors for at least 1 hour, but even better if time allows to cover and refrigerate for 4 to 6 hours, up to overnight. Longer time equals stronger flavors, which equals yum.
Make the Shrimp and Broth. Peel the shrimp and reserve the shells. Leave the tails on some shrimp. These are to hang over the rims of the glasses. It’s not necessary, but they are a pretty presentation.
Add the water, shrimp shells, salt, lemon slices, carrot, garlic, bay leaf, onion, peppercorns, and cilantro to a medium sauce pot. Bring it up to a boil, then lower the heat to maintain a gentle boil. Simmer for 10 minutes, stirring every once in a while, submerging the ingredients, and pressing the juice out of the lemon slices.
Strain the shrimp stock through a fine-mesh sieve into a 4-cup measuring cup or medium bowl. Discard the solids. Return the stock to the pot.
Bring the stock back to a boil over medium-high heat.
Add the shrimp and cook for about 1 ½ to 2 minutes, or until the shrimp are white and have curled into a loose “C.”
Remove the shrimp with a slotted spoon or spider strainer and place them into the ice bath to stop the cooking process.
Pour the stock into a heat-safe bowl. Pop it into the refrigerator for about 1 hour to cool.
While the shrimp are still chilling out and the shrimp stock has cooled, add the Homemade Clamato Juice to a large bowl. Add the stock, ketchup, lime juice, and hot sauce. Stir and taste. Adjust with any salt, pepper, lime juice, and/or hot sauce. Add the cucumber, onion, diced tomato, chile, and cilantro. Stir. Taste and adjust any seasonings.
Remove the shrimp from the ice bath and place them onto a few layers of paper towels. Pat dry. Chop the shrimp without tails into bite-size pieces. Add them to the tomato mixture. Stir.
If you would like the shrimp cocktail chilled (not room temperature), cover and refrigerate for 2 hours. Refrigerate the shrimp in the ice bath also.
Pit the avocado and dice into about ¼” pieces. Add to the shrimp cocktail.
Divide the mixture between 8 glasses. Divide the whole shrimp (tails on) onto the rims of the glasses. Sprinkle with cilantro and serve with tortilla chips and saltine crackers.