Cinnamon-Sugar Churros with Cajeta

Combine 2 cups water, butter, vanilla bean seeds and pod, cinnamon stick, orange zest, and salt in a large saucepan over medium; bring to a simmer, stirring occasionally. Let simmer until infused with cinnamon and vanilla, a few minutes. Remove and discard cinnamon stick and vanilla bean pod. Add flour all at once, and quickly stir with a heatproof spatula or wooden spoon until completely incorporated, about 20 seconds.

Immediately transfer mixture to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until slightly cooled and the steam dies down, about 3 minutes. Add egg, and beat on medium speed until completely incorporated, about 20 seconds. Transfer some of the batter to a double-lined pastry bag (place 1 bag inside another) fitted with a 1/3-inch open star tip, refilling bag as needed.

Pipe 14 (15-inch-long) straight ropes of batter onto 2 parchment paper–lined baking sheets. Alternatively, pipe dough in teardrop shapes, lightly pressing ends together to secure. Chill shapes at least 30 minutes or up to 2 hours. (Alternatively, freeze on baking sheets until hardened. Transfer to a large ziplock plastic freezer bag, and freeze up to 1 month. Cooktime will be the same)

Stir together sugar and remaining 1 tablespoon cinnamon in a large bowl; set aside. Pour oil to a depth of 2 1/2 inches in a large Dutch oven. Heat over medium-high to 375°F. Working in batches, fry chilled or frozen churros, turning occasionally, until the churros rise to top of oil and turn light golden brown with a crispy outside and custardy center, 2 minutes and 30 seconds to 3 minutes and 30 seconds, returning oil to 375°F between batches. Toss hot churros in cinnamon-sugar, and serve immediately with cajeta or sweetened condensed milk for dipping.