Preheat oven to 350 degrees.
Add the melted butter into the cake pan.
Evenly add 6 tablespoons of brown sugar to the pan.
Add the nectarine slices in a star pattern on top of the brown sugar and butter, making sure to fit as many as possible.
Sprinkle 2 additional tablespoons of brown sugar evenly over the nectarine slices, along with the freshly grated nutmeg. Set aside while preparing cake batter.
In a large bowl, combine the all purpose flour, baking powder, baking soda, and salt.
In another large bowl (of a stand mixer, or with a hand mixer), cream together the softened butter, granulated sugar, and brown sugar.
Add the egg, yogurt, milk, and vanilla and blend until combined.
Slowly blend the dry ingredients into the creamed mixture (scraping the sides down on occasion) until a thick but creamy batter is formed.
Use a spatula to spoon the cake batter gently and evenly over top of the nectarines in the cake pan.
Place the cake pan onto a baking sheet and bake the cake in a preheated oven for 50 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Cool the cake on a cooling rack for 10 minutes.
Place a serving plate on top of the cake (in the pan) and invert the cake pan, and plate, in one smooth motion so that the nectarine slices are now on top.
Gently remove the cake pan from the cake and allow the cake to cool completely.
Slice, serve and enjoy!