Preheat oven to 350°F (175°C). Grease a 12-cup* Bundt pan.
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 peanut butter and vanilla. Add the eggs, one at a time, mixing well after each addition.
Reduce mixer speed to low. Add the flour mixture in three portions, alternating with two portions of milk. Mix just until combined.
Transfer the batter to the prepared pan. Bake 60 to 70 minutes, or until a pick inserted into the center comes out clean.
Cool in the pan on a wire rack for 15 minutes. Then invert the cake onto a wire rack, remove the pan, and allow to cool completely.
To make the glaze:
Using an electric mixer on medium speed, beat the cream cheese, peanut butter, and confectioners' sugar until combined and smooth. Add 2 tablespoons milk and mix well. Add more milk, a small amount at a time, until the glaze is thick but pourable.
Top the cooled cake with glaze. If desired, top with chopped peanuts or other garnish.
Notes
*I've made this cake a few times, and I found that I had better success with a 12-cup pan than a 10-cup pan. It will fit in a 10-cup pan, but it's a little too full for my liking. If you have that bigger pan, I'd definitely go that route.