Prepare the pork tenderloin: Slice the pork into 1-inch thick medallions. Place each medallion between two sheets of plastic wrap and pound them until they are about 1/4 inch thick. Set aside.
Make the oyster cracker breading: In a food processor, pulse the oyster crackers until they are finely crushed but not powdered. Transfer the crushed crackers to a shallow dish.
Set up your breading station: In one shallow dish, whisk the eggs until well beaten. In another shallow dish, combine the flour, paprika, garlic powder, onion powder, salt, and black pepper.
Coat the pork tenderloin: Dip each pork medallion into the flour mixture, ensuring it is evenly coated. Shake off any excess. Next, dip the coated pork into the beaten eggs, allowing any excess to drip off. Finally, press the pork into the crushed oyster crackers, gently pressing to adhere the breading.
Pan-fry the pork tenderloin: In a large skillet, heat about 1/4 inch of vegetable oil over medium-high heat. Once hot, carefully place the breaded pork medallions into the skillet, being careful not to overcrowd the pan. Cook for approximately 3-4 minutes per side, or until the pork is golden brown and cooked through. Repeat the process for the remaining pork medallions, adding more oil as needed.
Assemble the sandwich: Drain the fried pork tenderloin on a paper towel-lined plate to remove excess oil. Meanwhile, lightly toast the hamburger buns. Place a piece of pork tenderloin on the bottom bun, and layer with your preferred toppings. Cover with the top bun. Enjoy!