Using a 5-inch round cookie cutter, cut a smaller tortilla out of each tortilla. Save the scraps for making chilaquiles, tortilla soup, etc. Heat 2 tablespoons of vegetable oil in a medium saute pan over medium-high heat. Then add the beans to warm and soften, about 5 minutes, stirring continuously to avoid burning. Turn the heat off and reserve.
In a large saute pan, heat the remaining 1/2 cup of vegetable oil to 350 degrees F. While the oil is heating, form the panuchos. Start by spreading 1 tablespoon of warmed beans on the surface of the tortilla. Stack the second tortilla over it pressing on the edges to seal. Remove the excess beans on the side of the panucho. Working in batches, fry the panuchos until golden in color, about 3 minutes per side. Remove from the pan and drain on a paper-towel-lined plate.