Preheat the oven to 350°F (180°C).

Grease a 9-inch (23-cm) square baking pan with 1 teaspoon of oil and line it with parchment paper. Leave some paper hanging over the edges of the pan to use as handles later. Set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, orange zest, and spices.

In a medium bowl, whisk together the milk, apple sauce, coconut sugar, oil, and maple syrup.

Make a well in the middle of the flour mixture then pour the mixed wet ingredients into the bowl of dry.

Using a rubber spatula or wooden spoon, gently fold everything together until just combined, with some streaks of flour remaining.

Add the grated carrot and chopped walnuts to the bowl. Continue to fold the batter together gently until just combined — a few streaks of flour are ok!

Spoon the batter into the prepared baking pan. Smooth the batter evenly into the pan using the back of the spoon.

Place the carrot cake in the preheated oven for 33 to 35 minutes, or until the top springs back when lightly touched, or a tester comes out clean.

Remove the cake from the oven, and place the pan on a wire rack to cool for 10 to 15 minutes.

Use the parchment paper handles to gently lift the cake from the pan. Remove the paper from the cake then place it on the wire rack to cool completely.