Preheat oven to 375°F (190°C) and line a muffin tin with paper liners.
In a large bowl, whisk together flour, baking powder, baking soda, salt, granulated sugar, and brown sugar.
In a separate bowl, mix peanut butter, egg, milk, melted butter, and vanilla extract until smooth and well combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Do not overmix.
Divide the batter evenly among the muffin cups, filling each about 3/4 full.
If desired, sprinkle oats, chopped peanuts, or chocolate chips on top.
Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean.
Allow muffins to cool for a few minutes before serving.