Preheat the oven to 350 degrees.
Grease the bottom and up about one inch of the sides of a 9 inch springform pan.
In a medium sized bowl, cream together the butter and sugar. Beat until light and fluffy. Add in the egg and vanilla, beating well again. Add the flour, baking powder and salt, mixing well.
Using the back of a spoon or a small spatula, spread the dough evenly over the bottom of the springform pan and about 1 inch up the sides.
Arrange the sliced peaches over the top of the dough like spokes of a wheel, placing them closely together.
In a small bowl, mix the remaining sugar and the cinnamon. Sprinkle it well over the peaches and dough.
Bake for 30-35 minutes at 350 degrees or until the edges of the kuchen are lightly golden brown.
Place on a cooling rack for 10 minutes before removing the sides of the pan.
Serve warm or after it's cooled.