Heat the corn-tortilla frying oil in an 8-inch skillet over medium heat to 350°F. Fry corn tortillas one at a time for 30 to 60 seconds per side until crisp and golden, keeping them flat with tongs, then drain on a rack. Set the frying pan safely aside.

Mix beef gently with cumin, ancho chile, 1/2 teaspoon salt and garlic powder. Shape into 4 round patties about 5 inches wide and 1/3 inch thick. Cook in a large skillet over medium-high heat in 2 batches for 3 to 4 minutes per side until each reaches 160°F, then transfer to a clean plate.

Mash avocado with lime juice and remaining salt. Warm flour tortillas in the microwave under a barely damp paper towel for 20 to 30 seconds until flexible.

Scatter one-quarter of the Pepper Jack in the center of each large flour tortilla and add one cooked beef patty. Place one crisp corn tortilla over the patty, spread with one-quarter of the avocado and add one-quarter of the cabbage.

Cover each filling stack with a small flour tortilla. Fold the large tortilla border inward in overlapping pleats, covering the patch edges and holding the packet seam-side down.

Wipe the large skillet and brush with 1 teaspoon wrap-toasting oil. Cook 2 packets seam-side down over medium heat for 2 to 3 minutes, then turn and cook for 2 minutes more until golden and sealed. Repeat with remaining oil and packets.

Rest for 2 minutes, cut each packet in half and serve one crunchwrap per person.