These will turn out fantastic. They’re best served warm or right off the frying pan.
This isn’t a recipe so much as a process.
You should have an assembly line that looks like the following:
Put about 15 shrimp through the assembly line. First dip them in the flour bowl, then dip them in the egg batter and let the excess drip off, then roll them in the coconut, and place them on the first paper towel if you don’t have room in the pan. Put the shrimp in the pan for about 2 minutes on each side. Watch the butter and add more as necessary to make sure there’s enough that it doesn’t start burning. Also watch the coconut flakes that fall off. They have a tendency to burn after a while, and then they stick to the new batches of shrimp and look bad, so occasionally you may have to just wipe the pan clean and start over with new butter. After the shrimp are lightly brown, take them out of the pan and put them on the far paper towel so they can dry off a little (that is, so the excess butter can soak into the towel).
Serve immediately.