Preheat the oven to 350°F. Thoroughly grease and flour a 10-inch Bundt pan, making sure to coat all the grooves.
In a medium bowl, whisk together the flour, baking soda, baking powder, salt, and cinnamon or pumpkin pie spice until evenly combined.
In a large bowl, beat the softened butter and brown sugar with an electric mixer until light and fluffy. Beat in the eggs one at a time, mixing well after each addition, then mix in the vanilla.
Add the dry ingredients to the butter mixture in two additions, alternating with the sour cream or Greek yogurt. Mix just until combined. Do not overmix.
Spread the batter evenly in the prepared Bundt pan. Bake for 37–40 minutes, or until a toothpick inserted into the cake comes out clean or with a few moist crumbs. Cool in the pan for 15 minutes, then carefully invert onto a wire rack and cool completely.
Beat the softened cream cheese and butter until smooth and creamy. Add the powdered sugar and vanilla and beat until combined. Add the milk and beat until smooth and spreadable, adding a little more milk if needed. Spread the cream cheese buttercream over the completely cooled cake, allowing some to fall naturally down the sides. Slice and serve.