Add refried beans, shortening, and milk to a medium saucepan over medium heat. Stir until smooth and heated through. Add 1 to 2 cups shredded cheese and stir until melted and creamy. Reduce heat to low and keep warm while preparing the tostada shells.
Add ½ inch of vegetable oil to a medium skillet and heat to about 350°F. Fry tortillas one at a time for 30 to 60 seconds on each side, or until crisp and golden.
Transfer fried tortillas to a paper towel-lined plate in a single layer. Sprinkle with salt while still hot.
Use ¼ to ⅓ cup beans per tostada. Spread a thin, even layer of warm refried beans over each shell, leaving a little space around the edge so the tostada is easier to pick up and the shell stays crisp.
Add shredded chicken, beef, or pork, then top with shredded cheese, sour cream, chopped tomatoes, and any other favorite toppings.
Serve immediately so the tostada shells stay crisp.