1. Begin heating 3 inches of oil in a medium saucepan over medium heat until it reaches 350 degrees.
2. While the oil is heating, combine the cabbage, carrots, vinegar, 1/4 teaspoon salt, and 2 tablespoons of mayonnaise in a medium bowl. Mix well and set aside.
3. Heat a cast-iron griddle or large skillet over medium-high heat. Cut the slider buns in half and place them cut-side down on the griddle.
4. Toast them until they are golden brown, which should take about 2 to 3 minutes. Then remove them from the heat and let them cool.
5. In a separate medium mixing bowl, whisk together the cornmeal, rice flour, basil, garlic powder, oregano, paprika, dry mustard, onion powder, white pepper, thyme, and 1 teaspoon of salt.
6. Place the beaten eggs in a small bowl. Take an oyster and dip it into the egg mixture, then coat it in the seasoned cornmeal mixture.
7. Repeat this process, returning the oyster to the egg mixture and then coating it with cornmeal again. Follow this process for all oysters.
8. Once the oil has reached 350 degrees, carefully place the oysters into the hot oil and fry them until they are golden brown, which should take about 3 minutes per side.
9. After frying, remove the oysters from the oil and place them on a paper towel-lined plate to drain.
10. To assemble the sandwiches, spread the remaining 4 tablespoons of mayonnaise on the cut-sides of the buns. Add a dollop of ketchup on the bottom bun, place a fried oyster on top of the ketchup, and then add 1 heaping tablespoon of coleslaw. Finally, cover with the top bun.