Combine the corn, eggs, flour and cream in a food processor and blend until the corn is finely chopped and appears creamy, scraping down the sides as needed. Remove to a bowl. Add the shrimp, celery, onions, cilantro, garlic, salt and pepper and mix well.
Heat the butter and oil in a large skillet.
For each cake, add a heaping tablespoon of the corn mixture to the skillet. Keep the cakes separated and press to flatten slightly.
Cook over medium heat until golden brown on the bottom, then turn and cook the other side until golden, about 3 minutes total.
Continue until all the cakes are cooked, placing them on a platter and keeping them warm. Serve as an appetizer or side dish, garnished with cilantro leaves, if desired.