In a large bowl combine masa harina, flour, baking powder, and salt. Gradually add the hot water, stirring until mixture forms a soft dough. Stir in cheese.
Divide masa mixture into 12 portions. On a lightly floured surface use your hands to pat each portion into a 2-1/2-inch round. As you work, keep dough and formed gorditas covered with clean kitchen towels or plastic wrap to keep them from drying out.
Pour oil into a heavy medium saucepan to a depth of 1-1/2 inches. Heat oil over medium heat until its temperature reaches 350 degrees F. Fry gorditas, three or four at a time, in hot oil about 2 minutes each or until crisp and golden brown. Drain on paper towels. Using a serrated knife, split hot gorditas horizontally to partly open.
In a medium bowl combine black beans, chile pepper, and garlic; use a fork to slightly mash bean mixture. Spoon bean mixture into gorditas; spoon in cabbage and salsa. Serve with lime wedges.