Slice the tomatoes crosswise into 1/2-inch slices.
In a shallow bowl, combine the cornmeal, salt and cayenne pepper. In another shallow bowl beat the eggs. Line a surface or large plate with paper towels.
Dip each tomato slices into the eggs, lift to allow excess egg to drip off, then place them in the cornmeal mixture, and turn to so that they are coated with the crumbs. Place on a wire rack as they are finished.
Fill a large skillet with oil to a depth of about 1/4-inch. Heat over medium high heat until barely shimmering. Add the tomatoes in a single layer, without crowding them (you will probably need to do this in batches). Fry them for about two minutes until they are golden on the bottom, then flip them and fry for another 2 minutes, until the other side is golden. Transfer the tomatoes to the paper towel lined plate or surface. Repeat until all of the tomatoes are cooked.
Serve the tomatoes hot or warm, with the salsa on the side.