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 cream the softened unsalted butter, creamy peanut butter, granulated sugar, and light brown sugar until light and fluffy, about 2-3 minutes.
Add the egg and vanilla extract to the butter mixture and beat until well combined.
Gradually add the dry flour mixture to the wet ingredients, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined; do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
Bake in the preheated oven for 16-18 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and allow them to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.