Preheat the oven to 350°F. Spray a Bundt pan with flour-based baking spray. Set aside.
In a small bowl, combine the milk and apple cider vinegar; set aside.
In a large bowl, use a mixer to cream together the butter and brown sugar. Add the pumpkin, milk mixture, and vanilla extract; continue mixing until incorporated. Set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, allspice, ginger, nutmeg, and salt. Add the flour mixture to the pumpkin mixture one cup at a time, mixing to incorporate each addition.
Transfer the batter to the prepared Bundt pan. Bake for 35 minutes, or until a toothpick inserted in the center comes out clean. Cool for 10 minutes on a wire rack then carefully invert the cake out of the pan and onto the wire rack. Cool completely.
For the frosting: In a small bowl, combine the milk, butter, and vanilla extract. Mix in the confectioners' sugar, brown sugar, cinnamon, and salt until incorporated. Drizzle over the top of the cake and serve.