Combine 1 (30-ounce) can beans, ¼ cup shortening, and ⅔ cup milk in a pot over medium heat.
Stir vigorously with a wire whisk until silky smooth.
Add 1½ cups cheese and let melt. Remove from the heat and set aside.
Heat ½ inch oil in a medium saucepan over medium-high heat. Fry tortillas one at a time for 30–60 seconds on each side, until golden. Place them in a single layer on a paper towel-lined plate to drain excess oil and sprinkle with salt.
When ready to serve, top each tortilla with beans, then add any desired toppings.