Preheat the oven to 350°F.
Grease a bundt pan thoroughly with butter or nonstick cooking spray. Ensure all the crevices are well-coated to prevent sticking.
In a large mixing bowl, cream together the unsalted butter, white granulated sugar, and light brown sugar until light and fluffy. Using a hand mixer or stand mixer, this should take about 3-4 minutes.
Add the eggs one at a time, mixing well after each addition.
Pour in the buttermilk, vanilla bean paste (or vanilla extract), and pumpkin puree. Mix until everything is fully combined and smooth.
In a separate bowl, whisk together the all-purpose flour, baking powder, pumpkin pie spice, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing at low speed until combined. Be careful not to overmix.
Pour the batter evenly into the prepared bundt pan, smoothing the top with a spatula.
Place the pan in the preheated oven and bake for 55-60 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Once baked, remove the cake from the oven and allow it to cool in the pan for 10-15 minutes. After cooling, carefully invert the cake onto a wire rack to cool completely.
In a medium bowl, whisk the softened cream cheese with a hand whisk until it becomes smooth and creamy.
Add the powdered sugar and vanilla bean paste, mixing until fully incorporated.
Gradually add 1-2 tablespoons of milk, one tablespoon at a time, until the glaze reaches the desired consistency—smooth and pourable.
Once the cake has cooled completely, drizzle the cream cheese glaze over the top, allowing it to drip down the sides.
Let the glaze set for a few minutes before slicing and serving.