Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined.
Gently fold in the sliced peaches.
In a medium bowl, combine the flour, brown sugar, granulated sugar, and cinnamon for the topping. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs.
Spread the cake batter evenly into the prepared baking pan. Sprinkle the crumb topping evenly over the batter.
Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean and the topping is golden brown.
Let the cake cool in the pan for at least 15 minutes before slicing and serving. Serve warm or at room temperature.
Notes
This peach crumb cake is delicious on its own, or served with a scoop of vanilla ice cream or a dollop of whipped cream.