Preheat the oven to 350 degrees F. Grease a bundt pan and dust with flour, making sure to shake out the extra flour. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, allspice, and salt. Set aside
In a separate medium-sized mixing bowl whisk together the pumpkin, buttermilk, and vanilla until evenly combined. Set aside
In the bowl of a stand mixer (or a large mixing bowl with a hand mixer), beat together the butter and sugar until light and fluffy, about 3-4 minutes. Add the eggs, one at a time, and beat on medium for 1 minute.
Reduce the speed of the mixer to low. Add 1/3 of the flour flour mixture, then 1/2 of the pumpkin mixture, and repeat. Then add in the last 1/3 of the flour mixture and mix until just combined. Set aside.
Cream Cheese Filling
In a medium mixing bowl, beat the cream cheese and sugar until light and smooth. Add the egg and beat until incorporated.
Beat in the lemon juice, vanilla, and flour until combined and smooth. Set aside.
Assembly
Pour 3 cups of pumpkin cake batter into the prepared bundt pan and smooth into an even layer.
Using the back of a large spoon, press into the cake batter to create a ditch for the cream cheese filling to fill. Carefully add the cream cheese mixture into the ditch, making sure that it stays in the center and doesn't touch the edges of the pan.
Carefully spoon the remaining cake batter over top of the cream cheese mixture and spread evenly over the top.
Bake
Bake for 45 minutes at 350 degrees F.
Reduce the heat to 325 degrees F and carefully cover the pan with foil. Bake for another 15-25 minutes or until a toothpick inserted into the center comes out clean. (There shouldn't be cake crumbs, but some cheesecake stuck on is okay.)
Remove the cake from the oven and allow to cool for at least 10 minutes. Then invert onto a wire rack, remove the pan, and allow the cake to completely cool.
Icing
In a small bowl whisk the powdered sugar and buttermilk together until smooth. (I start with 2 tablespoons of buttermilk and add more as needed to thin the glaze.)
Drizzle the glaze over the cooled cake before slicing and serving.