Preheat the oven to 350ºF and generously grease a 9×13-inch cake pan. In a mixing bowl, cream together the softened butter and brown sugar until light and smooth. Blend in the milk, peach syrup, and vanilla extract until thoroughly incorporated. In a separate bowl, whisk together the flour, baking powder, and salt, then gradually add this dry mixture into the wet batter, stirring just until combined. Gently fold in the chopped peaches, taking care not to overmix. Pour the batter into the prepared pan and spread evenly. Bake for 25 minutes in the center of the oven, or until a toothpick inserted into the middle emerges clean. Allow the cake to cool completely in the pan.

For the icing, place the butter, cream, and brown sugar into a small saucepan and bring to a boil over medium heat. Remove from heat and immediately whisk in the vanilla and powdered sugar until smooth and glossy. Quickly spread the icing over the cooled cake, as it begins to set rapidly. Let the icing firm up before slicing and serving.