Prep your pan and oven: Heat the oven to 350°F (175°C). Grease an 8-inch square pan or a 9-inch round pan and line the bottom with parchment for easy release.
Whisk dry ingredients: In a large bowl, whisk the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
Mix the wet ingredients: In another bowl, whisk the eggs, maple syrup (or honey), olive oil, yogurt, and vanilla until smooth.
Combine gently: Pour the wet mixture into the dry.
Stir with a spatula until just combined. Do not overmix or the cake can turn dense.
Fold in apples and nuts: Stir in the chopped apples and nuts (if using) until evenly distributed.
Fill the pan: Spread the batter into the prepared pan. If you like, sprinkle the top with turbinado sugar for a crisp finish.
Bake: Bake for 28–35 minutes, or until the center springs back and a toothpick comes out with a few moist crumbs.
Cool: Let the cake cool in the pan for 10 minutes, then run a knife around the edge and transfer to a rack to cool completely.
Serve: Enjoy plain, dust with a little cinnamon, or top with Greek yogurt or a dollop of lightly sweetened whipped cream.