In a large, heavy-bottomed saucepan, bring 3 1/2 cups water to a boil and add the sugar. Cook for 1 minute and, whisking, add the flour in a steady, slow stream. When the mixture becomes too thick for the whisk, change to a wooden spoon and continue to cook over low heat for 15 minutes. Pour the mixture out onto a marble counter and allow to cool.

Heat the oil to 375 degrees F in a large heavy-bottomed pan. Knead the dough by hand for 8 minutes. Roll it out into a rope (a dowel), about 1/3-inch thickness. Cut the dowel into lengths of about 6 inches, and form doughnut-shaped rings that should be equal in diameter to a tennis ball. Fry them in the oil until firm and golden, 7 to 8 minutes, then remove from the oil with a slotted spoon or spatula. Drain on a plate lined with paper towels.

While the doughnuts cool, in a small, heavy-bottomed saucepan, combine the honey and the orange flower water and heat over medium heat to achieve the viscosity of a thin syrup. Dip each doughnut in the honey mixture, shake off the excess syrup and sprinkle with the powdered sugar.