Preheat oven to 325°F. Spray a 10-inch bundt pan with non-stick cooking spray. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese and butter on medium speed until smooth, about 3 minutes.
Gradually add the brown sugar and granulated sugar, mixing until light and fluffy, about 2-3 minutes.
Add the eggs, one at a time, mixing well after each addition.
Add the maple extract and mix until well combined.
With the mixer on low speed, gradually add the cake flour, mixing just until the flour is fully incorporated.
Mix in buttermilk until just combined. Scrape down the sides of the bowl to ensure everything is mixed well.
Pour the batter into the prepared bundt pan and smooth the top with the spatula. Bake for 75-80 minutes, starting to check for doneness at 1 hour by inserting a toothpick into the center of the cake. If it comes out with just a few crumbs but no wet batter, it's done. The cake should have a deep golden brown crust on the edges and a lighter center.
Once baked, let the cake cool completely in the pan before inverting onto a serving plate.
While the cake cools, prepare the maple glaze. In a small saucepan over medium heat, combine the unsalted butter, maple syrup, and heavy whipping cream. Bring the mixture to a boil and continue boiling for 1 minute.
Remove the pan from heat and immediately whisk in the confectioners' sugar until smooth. Let the glaze cool for 25-30 minutes, or until it has slightly thickened.
Once the cake has cooled and the glaze has thickened, drizzle the glaze evenly over the cake.
Let the glaze set slightly before serving.