In a large mixing bowl, cream together the 1 cup butter and sugar with an electric mixer (or stand mixer) until light and fluffy. Beat in the vanilla, then add the eggs one at a time. Turn the mixer to low speed and mix in the buttermilk until just combined. The mixture will look curdled. Using a sifter or fine-mesh strainer, combine the flour, baking powder, baking soda and salt in a separate medium bowl. Stir, in three stages, into the wet mixture until combined; set aside.
Place the 1/2 cup butter into a 9- x13-inch baking pan and melt in the oven. Remove pan from the oven and stir in the brown sugar and oats. Spread evenly throughout the bottom of the pan. Layer the peach slices evenly across the pan, on top of the sugar/oat glaze.
Pour the cake mixture over top of the layered peaches. Spread evenly with a spatula. Tap the pan several times on the counter top to rid any air bubbles. Bake in the preheated oven for 45 to 55 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven, and immediately invert onto a large serving plate. Allow to cool, then serve.