- Place a rack in the oven about 8 inches from the heat source; preheat broiler. Arrange jalapeños on a baking sheet and broil, turning occasionally, until charred and softened but still somewhat firm, 7 to 8 minutes. The jalapeños can also be roasted over the open flame of a gas stove burner. Transfer to a heatproof bowl, cover tightly with plastic wrap, and set aside for 10 minutes.
- Working carefully, use a paring knife to scrape off and discard as much jalapeño skin as possible. Make a cut down 1 side of each jalapeño and remove ribs and seeds with a small spoon, being careful not to tear peppers further. To fill each jalapeño, firmly press together 1/4 cup cheese in the palm of your hand to form an oblong mass, then stuff inside jalapeño; set aside.
- Pour oil into a large pot and heat over medium-high until oil registers 375 degrees on a deep-fry thermometer. Meanwhile, in a large bowl, whisk together masa harina, chili powder, 1 1/2 teaspoons salt, and 2 3/4 cups water. Put flour in a wide, shallow dish.
- Working in batches, roll jalapeños in flour, shaking off excess; then hold each by the stem and dredge in batter to coat completely. Carefully drop jalapeños into hot oil by their stems and fry, turning occasionally, until deep golden brown, 4 to 5 minutes. Transfer to a paper-towel-lined plate, season with salt to taste, and serve warm.