Put the cornflour on a plate and season with salt and pepper, and put the breadcrumbs on another plate.
Lightly beat the eggs in a shallow bowl.
Dust the snapper fillets in cornflour, dip into the egg, and then coat with breadcrumbs. Set aside on a plate.
Heat the oil, garlic and rosemary in a frying pan until very hot. If you like, add butter for extra flavour and colour. Cook the snapper fillets for about 2 minutes on each side, until golden brown. You may need to do this in more than one batch, depending on the size of your pan. Remove from heat and place on a plate lined with paper towels.
Drain the oil, and keep the garlic and rosemary for the balsamic reduction.
Remove any breadcrumbs from the pan, then add balsamic vinegar and simmer for about 4 minutes, until the liquid has reduced by a third. Add lime or lemon juice, and season with salt and pepper to taste.
Serve snapper with sauce on the side for drizzling.