Heat the oil in a Dutch oven to 375 degrees F.
Fry 4 pieces of plantains until they float to the surface, about 2 minutes.
Drain on a paper towel and repeat with the remaining 4 pieces.
Using 2 wooden cutting boards or a heavy pan, flatten each piece of plantain.
Refry each piece of flattened plantain, in batches, until golden, about 4 minutes.
Season with salt and pepper and a little granulated garlic.
Set aside on a paper towel.
For the sandwich build:On the bottom of 4 fried plantains (or tostones), place a slice of American cheese, a quarter of the ham, a quarter of the tomatoes and 1 lettuce leaf.
Spread the Garlic Mayo on the top tostones and close.
Cut in half on the bias.
Pick up gently but bite aggressively.
For garlic mayo:In a bowl, mix together the mayo, chili powder, cumin, garlic and a little salt and pepper to taste.