Step 1

Preheat the oven to 350F. Grease an 8-inch square baking pan.

Step 2

Put the flour, brown sugar, cinnamon, baking powder, baking soda, and salt into the baking pan. Use a fork to thoroughly mix the ingredients together.

Step 3

Use your hands to make a hole in the center of the dry ingredients. Into the hole, crack the egg and add the olive oil, yogurt, applesauce, and vanilla. Use a fork to mix the ingredients together until smooth and blended. Smooth the top of the batter with the side of a butter knife.

Step 4

Bake until the cake is fairly firm when you press lightly at its center and a toothpick inserted in the middle has no wet batter sticking to it, 25 to 30 minutes.

Step 5

Remove from the oven and leave on the counter to cool completely, 1 hour. Leave the cake in the pan. Dust with powdered sugar. Cut into pieces and use a small spatula to lift them from the pan.