1 pound nopales (fresh cactus paddles)—thorns removed, paddles peeled and
sliced 1/4 inch thick (see Note)
2 jalapeños, sliced crosswise 1/4 inch thick
1/4 cup kosher salt
2 cups water
1 cup apple cider vinegar
3/4 cup sugar
1 teaspoon sweet pimentón de la Vera (smoked Spanish paprika)
In a large bowl, toss the cactus paddles and jalapeños with the salt and let stand for 45 minutes. Drain well. Transfer the cactus and jalapeños to a heatproof bowl.
In a medium saucepan, combine the water with the vinegar, sugar and paprika and bring to a boil. Pour the brine over the cactus and jalapeños and stir well. Let cool to room temperature, then cover and refrigerate for 2 days before serving.
The pickled cactus and jalapeños can be refrigerated for up to 1 week.
Most nopales are sold with the spikes removed; any stray spikes can be removed with a sharp paring knife.