Cook the shrimp in a hot oiled pan, 1 to 2 minutes per side. Remove and set aside to cool.
Add egg to a bowl and whisk.
Add hominy and cheese, stir to combine.
Add flour, corn meal, baking soda, and 2 tbsp of water. Mix into a batter.
Divide into six equal parts (if not eating immediately, set aside half the batter). Cook 4 to 6 minutes per side.
Cut cooled shrimp into 2 to 3 pieces each.
Add cilantro to salad and toss. Top with shrimp.
Serve fritters along with the salad.