Preheat the oven to 425 degrees F.
In a large saucepan, bring the water, butter, salt and granulated sugar to a rolling boil over medium high heat. When it boils, immediately take the pan off the heat. Stirring with a wooden spoon, add all the flour at once and stir hard until all the flour is incorporated, 30 to 60 seconds. Return the pan to the heat and cook, stirring, 30 seconds to evaporate some of the moisture.
Scrape the mixture into a mixer fitted with a paddle attachment. Mix at medium speed. With the mixer running, and working 1 egg at a time, add 3 of the eggs, stopping after each addition to scrape down the sides of the bowl. Mix until the dough is smooth and glossy and the eggs are completely incorporated. The dough should be thick, but should fall slowly and steadily from the beaters when you lift them out of the bowl. If the dough is still clinging to the beaters, add the 1 more egg and mix until incorporated. Stir in the orange flower water.
Using a pastry bag fitted with a large plain tip, pipe the dough onto the baking sheet, in 1-inch kisses. Whisk the remaining egg with 1 1/2 teaspoons water. Brush the surface of the dough with the egg wash (you may not use all the egg wash). Sprinkle with the French coarse sugar. Bake 15 minutes, then reduce the heat to 375 degrees F and bake until puffed up and light golden brown and have no more yellow pastry color showing, about 20 minutes more. Try not to open the oven door too often during the baking. Let cool on the baking sheet.
NotesThis is like a classic pate a choux (the X is left off because it is one word, unlike choux-fleur) or cream puff dough but with double the sugar and a touch of orange flower water. The tops are egg washed and then sprinkled with distinctive white coarse French sugar and baked. They are left unfilled and just eaten in the morning or for "Quatre heure" or "Le goûter", the after school snack at 4:00 by the dozen. You never eat or buy just one.