Fill a deep-fryer or large Dutch oven halfway with vegetable oil and heat to 350 degrees F.
Mix the sugar and cinnamon together in a large shallow bowl, set aside.
Combine the butter, water and sugar in a large saucepan over medium-high heat and bring to a boil. Once it has come to a boil, lower to a medium heat and add the flour, orange zest and nutmeg, stirring constantly until it comes away from the pan and it forms a ball. Transfer dough to a bowl and use an electric mixer to help cool it off. At this point you can whisk in the eggs, 1 at a time, until it becomes a smooth batter. Transfer the mixture into a large piping bag fitted with a large star tip. Working in batches, carefully pipe 4-inch long ribbons directly into the hot oil to fry. Fry until golden, turning if necessary, about 2 to 3 minutes. Remove with tongs and drain on paper towels. Transfer the churros into the sugar/cinnamon mixture and toss to coat. Serve immediately while still warm.
*Addition by Food Network Kitchens after show aired.