Preheat the oven to 350°.
Butter a 10-inch round cake pan. In a large saucepan, bring the maple syrup to a boil over high heat, then simmer over low heat until it thickens and is reduced to 3/4 cup, this should take about 20 minutes. Pour the syrup into the cake pan. Arrange the apples in the pan slightly overlapping them.
In a bowl, whisk the flour, baking powder, baking soda and salt. In a glass measuring cup, whisk the eggs with the buttermilk and vanilla. In the bowl of a standing electric mixer fitted with the paddle, beat the butter and sugar at medium speed until fluffy, for about 3-4 minutes.
Pour the dry ingredients into the wet ones in alternating batches. Scrape the batter over the apples and spread evenly. Bake the cake for 1 1/2 hours, until golden on top and an inserted toothpick comes out clean.
Allow the cake to cool down on a rack for 30 minutes. Place a plate on top of the cake and invert the cake onto the plate; you might need to tap the top lightly to release the cake. Let the cake cool slightly, and its ready to be served.