In a medium saucepan over high heat, combine dark brown sugar, heavy cream, and a pinch of kosher salt. Stir continuously for about 5 minutes until the mixture thickens and bubbles. Once the caramel reaches a glossy, thick consistency, remove it from the heat. Add unsalted butter and vanilla extract, stirring until completely melted. Allow it to cool slightly before transferring to an airtight jar.

In a shallow dish, mix together cane sugar, pumpkin spice, and a pinch of kosher salt to create the spiced sugar mixture. Set this aside as you will use it to coat the churros once they are fried.

In a medium saucepan over medium heat, combine water, sugar, a pinch of salt, and unsalted butter. Stir until boiling, then reduce the heat to low. In a separate bowl, whisk together unbleached all-purpose flour, pumpkin spice, and cinnamon. Carefully add the flour mixture to the boiling mixture, stirring vigorously until it forms a coherent dough ball. Allow it to cool for about 5 minutes.

Incorporate a beaten large egg and a splash of vanilla extract into the dough mixture. Mix thoroughly until you achieve a smooth and consistent dough, ensuring there are no lumps.

In a deep skillet, heat canola oil to 350°F (175°C). Using a piping bag fitted with a star tip, pipe 5 to 6-inch lengths of churro dough into the hot oil. Cut the dough with scissors, frying for about 2 minutes on each side until golden brown.

Immediately after frying, roll each churro in the spiced sugar mixture, coating them generously. Serve warm with the brown sugar caramel for dipping.