Cook the nopales. Scoop the nopales into a 2- to 3-quart saucepan, sprinkle generously with salt, then set over medium heat and cover (if your saucepan doesn’t have a lid, use a cookie sheet). When the nopales have exuded enough of their sticky sap to mostly cover the bottom of the skillet, about 5 minutes, uncover and continue cooking, stirring regularly, until all the liquid has evaporated, 5 to 7 minutes longer. Cool to room temperature and scoop into a bowl.
Finish the salad. Scoop the onion into a strainer and rinse with cold water, shake off the clinging moisture, then add to the bowl with the nopales. Add the tomato, serrano and cilantro. Taste and season with salt, usually about 1 teaspoon.
Serve the tacos. Set out warm tortillas, nopal salad, avocado, fresh cheese, chicharrón and limes for everyone to make their own tacos.