In a saucepan over medium-low heat, blend the milk with a half-cup of water. Cut the butter into chunks and add it to the water. When the water comes to a boil, remove it from the heat.
Add the flour and stir it into the liquid with a wooden spoon until well blended. Return to low heat and continue to stir until the mixture pulls away from the sides of the pan.
Remove the pan from the heat again and add two of the eggs, stirring quickly to blend into the batter. Stir in the other eggs, one at a time, and keep stirring until smooth and completely blended. Turn the batter out into a metal bowl to cool.
Combine the crawfish tails, green onions, and corn in a bowl. Add pinches of salt and pepper and toss to distribute the ingredients equally.
When the batter is cool enough to handle, scoop up a heaping tablespoon and form it into a ball. Push your finger into its center to form a well. Put a scant teaspoon of the crawfish mixture into the well, and close the ball up, working it with your fingers a little until some of the contents start poking out a little.
When you have about eight or ten beignets made, start frying them at 350 degrees. If they're close to round, you won't need to turn them. They take six to eight minutes to fry to a medium brown.