Preheat the oven to 375°F. Thoroughly grease and flour a 9-inch round baking pan and set aside.

In a small saucepan, combine the brown sugar and water and heat until the sugar has melted and the mixture starts to bubble. Remove from the heat and whisk in the butter until fully melted, then add the balsamic glaze and whisk until combined.

Arrange the peach slices on the bottom of the prepared pan, then pour the warm brown sugar mixture over the top of the peaches, tilting the pan to coat the peaches evenly. Set aside while you prepare the batter.

Combine the flour, baking powder, baking soda, and salt in a medium bowl. Set aside.

With an electric mixer or stand mixer, beat the eggs and sugar together in a large bowl until light yellow and fluffy, 3-5 minutes. Add the olive oil and vanilla and continue to beat until fully incorporated.

Add in the flour mixture and beat until a few dry streaks remain, then add the milk and continue beating just until incorporated evenly. Do not overmix.

Pour the cake batter over the peaches and smooth the top. Bake for 35-45 minutes, until deeply brown on top and a toothpick inserted into the center comes out clean.

Remove from the oven and allow to cool for 10 minutes, then run a knife around the edge of the pan and flip onto a plate*. If some peaches stick to the pan, gently place them back on top of the cake.

Serve while warm or at room temperature. Keeps for up to 3 days in an airtight container in the refrigerator.