Preheat your oven to 350°F. Lightly spray a 9x5-inch loaf pan with oil, then line it with a strip of parchment paper, allowing the edges to hang over the sides for easy removal.
In a small bowl, whisk together the flour, baking powder, baking soda, salt, chai spice, and cinnamon until well combined. Set aside.
In a large bowl, use a mixer to cream the butter and sugars together until light and fluffy, about 2-3 minutes. Add the eggs, vanilla extract, and applesauce one at a time, mixing well after each addition.
Gradually stir half of the dry mixture into the wet ingredients, then add half of the apple cider. Repeat with the remaining dry mixture and apple cider, mixing until everything is well combined.
Pour the batter into the prepared loaf pan and smooth the top with a spatula. Bake for 40-50 minutes, or until a toothpick inserted in the center comes out mostly clean and the top springs back slightly when gently pressed.
While the cake is warm, lightly brush the surface with apple cider. Combine about 3 tablespoons of sugar with ¼ teaspoon of chai spice, then sprinkle it evenly across the top for a spiced, sugary finish.
Allow the cake to cool in the pan for around 30 minutes before transferring it to a cooling rack. Once cooled, slice and enjoy!