Add all the ingredients for the batter, except for water, to a large low rimmed bowl. Mix them out with a fork so they are evenly distributed, and then add water in parts. Don't add the whole cup at once because your batter may become too thin, or you may even need extra water. Your batter should be reminiscent of runny pancake batter.
Heat a large frying pan to medium heat, and add enough oil to fill to about 1/4 inch height. The pan is ready when the oil dimples. If you're not sure, add a little drop of batter and see if it sizzles.
Drop a few of the heart of palm pieces in the batter, turn with fork so they are completely covered, then lift with fork to allow the excess batter drip off. One by one, carefully place pieces into hot pan. Be sure not to overcrowd your pan. For my 12 inch skillet, I added 6-7 pieces, so a 10 inch standard skillet should hold about 5.
After about 2 minutes, they should be brown and you can flip them to cook the other side. I have a hard time telling you how long you should cook each side for, other than "until a nice light brown color", because everyone's stove and pan will cook differently. Even with myself, each pan or burner I use affects cooking time and oil temperature, so keep an eye on it, and you'll get the hang of it after a few tries.
Place finished hearts of palm in a plate with a kitchen cloth or paper towels to absorb oil, so they don't become soggy. Continue frying until all your hearts of palm are finished.