Preheat the oven to 300°F (150°C), or 350°F (180°C) if your oven runs cool. Grease a large 12-inch Bundt or tube pan generously with cooking spray and set aside.
In a small bowl, combine the brown sugar, cinnamon, and nutmeg.
Pour the melted butter and bourbon or rum into the bottom of the pan. Arrange half of the peach slices on top of them. Sprinkle half the cinnamon sugar mixture over the peaches. Set it aside.
Cream the butter, cream cheese, and sugar at high speed in a stand or hand mixer until fluffy and looking white, 3-5 minutes.
Beat in the eggs, one at a time, until combined and smooth.
Mix flour, baking powder, and salt into the batter, followed by the milk and vanilla extract. Stir well until everything is thoroughly combined and smooth, scraping down the sides of the mixing bowl.
Spoon half of the batter into the cake pan over the peach slices and spread it out with a spatula. Then add the remaining peaches, sprinkle them with the remaining brown sugar mixture, and top it off with the remaining cake batter.
Tap the pans on the work surface to eliminate large air bubbles. Bake at 300℉ (150℃) until a tester inserted into the center comes out clean. It usually takes around an hour.
Remove from the oven and let it rest in the pan for about 10 minutes. Transfer the cake to a plate and let it cool completely (around 3 hours).
While the cake is cooling, make the glaze by mixing the confectioners' sugar, vanilla extract, and milk until smooth. Add a few drops of milk if too thick, and a little more sugar if too thin. You'll want it thin enough to drizzle, but thick enough to stay on the cake.
Drizzle as much as you like over the cake with a fork or spoon. Slice and serve.