Rinse the fresh cactus paddles under cold water, being careful not to prick your fingers with the small thorns on its surface. Using a vegetable peeler or small sharp knife, peel away the darker bumps where thorns grow, as well as the thorns, trying not to peel off all the outer dark green skin.
Lay the paddles flat on a chopping board, then trim around approximately 1/4 inch of the edges and 1/2 inch of the thick base. Once cleaned, rinse and dice into 1/2 to 1 inch-sized squares, to your liking.
Heat the oil in a thick, large-sized skillet (one that has a lid, since we will need it later on) over medium-high heat. Add the diced cactus, stir in the salt and stir for a minute or two. Place the lid on the skillet.
Reduce the heat to medium and let the cactus cook and sweat for about 20 minutes, until it has exuded a gelatinous liquid that will begin to dry out. Take the lid off the skillet, stir and make sure most of that gelatinous substance has dried up. If it hasn’t, let the cactus cook for a few more minutes until it does. Let the cactus cool and they are ready to go in a thousand directions including inside of a tortilla.