In a large saucepan under high heat, combine water, salt, sugar, nutmeg, cinnamon stick and vanilla. Allow to come to a rolling boil, stir and remove cinnamon stick. Reduce heat to low.
Add flour all at once and stir vigorously with a rubber spatula until mixture comes together and it’s smooth. Remove from heat and allow the mix to cool.
Heat about 2 inches of vegetable oil in a deep large frying pan over medium-high heat to 365 degrees.
Transfer to a 16-inch piping bag fitted with a rounded star tip (no bigger than 1/2-inch). Carefully pipe mixture into heated oil, about 6-8 inch length each, cutting ends with kitchen shears or sharp knife.
Remove each churro carefully and place on a paper towel lined plate to drain. While still hot, toss in sugar and cinnamon mixture. Serve hot.