Position a rack on the upper most shelf of the broiler element and preheat. Put the chiles on a foil-lined broiler pan and broil, turning occasionally with tongs, until the skin is charred, about 10 minutes. Transfer the chiles to a bowl, cover, and cool for 10 minutes.

Carefully rub the charred skin off the chiles. Using a small knife, make a lengthwise slit along the side of each chile to form a pocket. Carefully cut out and discard the seeds.

Cut the cheese into 6 (¼-inch-thick) slabs, about ¾ the length of each chile. Slip the cheese pieces into the pocket of each chile so they’re ⅔ full. Sew each chile shut with a wooden skewer or long toothpick.

Whisk the flour, baking powder, cumin, and salt in a large bowl. Stir in the beer to make a smooth batter.

In a large, wide, heavy-bottomed pot, pour in the oil to a depth of about 3 inches. Heat over medium heat until a deep-fry thermometer inserted in the oil registers 365 degrees F.

Put the flour for dredging on a plate. Working in 2 batches, dredge the chiles in the flour, dip in the batter, and carefully add to the oil. Fry, turning the chiles once, until golden brown and crispy, about 4 minutes per batch. Using tongs, transfer the chiles rellenos to a dry paper towel-lined baking sheet to drain. Sprinkle with salt, to taste. Gently pull out and discard the skewers.

Heat the sauce. Spoon some of the sauce on a plate and set 1 chile relleno on top. Repeat with the remaining sauce and chiles. Serve.