Using a small paring knife, clean the cactus paddles by scraping thorns or spines from both sides. Trim off the edges and any blemished or discolored areas. Wash well with cold water.
Cut the paddle lengthwise into half-inch thick strips and then cut crosswise into 1 to 1 1/2-inch lengths.
In a saucepot over medium heat, combine garlic, about 1 teaspoon of salt, and enough water to cover nopales. Bring to a boil.
Add nopales and cook for about 20 to 25 minutes or until nopales have changed color and are tender yet crisp.
Drain nopales and rinse well under very cold water. Rinse again as needed to rid of mucilage.
In a skillet over medium heat, heat oil. Add onions and cook until softened.
Add nopales and cook for about 2 to 3 minutes.
Add eggs and cook, stirring regularly, until eggs are set but still slightly wet. Season with salt and pepper to taste.
. Remove from heat, garnish with chopped cilantro and serve with warm tortillas.