Preheat oven to 325°F (165°C) and thoroughly grease and flour a 10-inch Bundt pan.
In a medium bowl, combine peach slices, 1/4 cup brown sugar, cinnamon, and cornstarch; stir to coat and set aside.
In a large bowl, cream together softened butter, cream cheese, and granulated sugar for 5 minutes until pale and fluffy.
Incorporate eggs one at a time, beating well after each addition and scraping down the sides of the bowl.
Stir in the vanilla extract and salt.
Gradually fold in the 3 cups of flour on low speed until the batter is smooth and just combined.
Prepare the crumble by mixing 1/2 cup flour, 1/2 cup brown sugar, and cold butter until it reaches a sandy, pea-sized texture.
Pour half of the cake batter into the prepared pan, layer the peach mixture over the batter, and cover with the remaining batter.
Sprinkle the crumble mixture evenly over the top of the batter.
Bake for 75 to 85 minutes, or until a long skewer inserted into the center comes out clean.
Allow the cake to cool in the pan for 20 minutes before carefully inverting onto a wire rack to cool completely.