In a medium saucepan, combine 1 cup water, the butter, brown sugar and salt over medium-high heat until it just begins to boil. Using a wooden spoon, stir in the flour until incorporated; remove from the heat. Stir for a minute, then beat in the eggs, 1 at a time, until the dough is glossy and smooth. Stir in the orange peel.
Fill a large saucepan with enough oil to reach a depth of 1 inch; heat until a deep-fry thermometer registers 350 degrees . Working in batches of 10, drop in rounded teaspoonfuls of the dough and cook, turning, until golden, about 5 minutes per batch; using a slotted spoon, transfer to paper towels to drain.
In a brown paper bag, combine the granulated sugar and cinnamon. Working in 4 to 5 batches, add the fritters and shake to coat.