Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, use an electric mixer to beat the softened unsalted butter, creamy peanut butter, granulated sugar, and light brown sugar together until creamy and smooth, about 2-3 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Alternately add the dry ingredients and the whole milk to the peanut butter mixture, beginning and ending with the dry ingredients. Mix until just combined; do not overmix.
Divide the batter evenly among the prepared muffin cups, filling each about 3/4 full.
Bake for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.