Preheat your oven to 350°F (175°C) and grease a 9x5-inch loaf pan. In a large mixing bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt, then set aside.
In the bowl of a stand mixer (or using a handheld electric mixer), beat the softened butter and sugar together until light and fluffy, scraping down the sides of the bowl as needed. Add the eggs one at a time, mixing well after each addition.
Lower the mixer speed and add one-third of the dry ingredients to the butter mixture, mixing just until combined. Add half of the buttermilk and mix again, increasing the speed slightly to ensure everything is incorporated. Repeat with another third of the dry ingredients, then the remaining buttermilk, and finally the last portion of the flour mixture. Beat just until the batter is smooth and well combined—do not overmix.
Pour half of the chocolate batter into the prepared loaf pan. Carefully spoon the cream cheese filling into the center of the chocolate batter, aiming to keep the cream cheese mixture in the middle. Gently pour the remaining chocolate batter over the top, spreading it to fully cover the cream cheese layer.
Bake the loaf in the preheated oven for 50–55 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs. Let the cake cool slightly in the pan, then pour the chocolate glaze over the top.
Cream Cheese Filling
In a medium mixing bowl, beat the softened cream cheese until smooth and fluffy. Add the egg, sugar, and vanilla extract, then beat until the mixture is creamy and well blended.
Chocolate Glaze
In a medium saucepan over medium heat, melt the butter. Whisk in the cocoa powder and milk, stirring continuously until the mixture is smooth and lump-free. Turn off the heat and gradually whisk in the icing sugar until the glaze is silky and completely smooth.