You will need two pots, one for the shrimp, one for the nopalitos. Place 2 quarts of the water or stock in each pot. In one pot place half the onion, half the garlic, and 1 tsp. each of salt and pepper.

In the other pot place the other half of the onion and garlic, 1 tsp. each of salt and pepper, and the lemon halves, squeezing the juice out into the pot and placing the entire lemon with the skin and everything. Bring both pots of water to a boil.

In the pot with the lemon add the shrimp, and add the nopalitos to the other pot. Cook both the shrimp and the nopalitos for about 10 minutes, until they are tender and cooked through.

Separately drain and cool both the shrimp and nopalitos.

In a mixing bowl, combine the cooled nopalitos, tomatoes, radishes, lime juice, cilantro, cumin, jalapeno, salt and pepper. Peel the shrimp and add to the nopale cocktail mixture, and mix well until everything is blended.

Cover and let sit in the refrigerator for a couple hours.

To serve, spoon the mixture into cocktail glasses and garnish with fresh avocado or lemon.