Preheat oven to 350° F and line 2 cupcake/muffin tins with cupcake liners.
In the bowl of a stand mixer, or using electric mixer, cream together butter and brown sugar. Beat in peanut butter, eggs and vanilla. Add oil and milk and mix until combined.
Add flour, baking soda, baking powder, and salt and mix until just incorporated; making sure not to over-mix.
Scoop out mixture into prepared cupcake tins, filling each 2/3 full. Bake at 350° F for 18-20 minutes or until toothpick inserted in center comes out clean.
Allow to cool completely before frosting.
Frosting
Using electric beaters, or a stand mixer, beat together butter peanut butter, and vanilla extract until light and fluffy.
With the mixer on low, add powdered sugar 1 cup at a time. Mix until the powdered sugar is fully incorporated and frosting is light and fluffy.