Whisk together the flour, baking powder, baking soda, and salt. Set aside.

Using an electric mixer on medium speed, beat the butter, brown sugar, and sugar until light and fluffy. Mix in the cookie butter and vanilla extract. Add the eggs, one at a time, mixing well after each addition.

Reduce the mixer speed to low. Add the flour mixture in three portions, alternating with two portions of milk. Add the sour cream with the second portion of milk. Mix just until combined.

Transfer the batter to the prepared pan. Bake 60 to 70 minutes, or until the cake has browned and a pick inserted into the center comes out clean.

Place the pan on a wire rack, and allow the cake to cool for 15 minutes. Then invert the pan onto a wire rack to remove the cake and allow it to cool completely.

Using an electric mixer on medium speed, beat the cream cheese, butter, and cookie butter until thoroughly combined and smooth. 

Add the confectioners’ sugar, and mix well. 

Mix in 2 tablespoons of the milk. Add more milk, a small amount at a time, until the glaze has a thick but pourable consistency.

Spoon or slowly pour the glaze over the cooled cake, letting it drip down the sides. Garnish with speculoos cookie pieces.