Preheat oven to 350F. Lightly grease and line a 8x8" baking pan with parchment paper.
In a mixing bowl, whisk together the olive oil, brown sugar, vanilla extract, eggs, and egg yolk on medium-high speed for 2-3 minutes, until creamy.
In a separate bowl, mix together the flour, baking powder, salt, and ground nutmeg.
On low speed, mix the flour mixture into the olive oil mixture until well-combined.
Evenly spread the batter in the prepared baking pan, then bake for 10 minutes.