Preheat the oven to 350°F (175°C). Line a baking tray with parchment paper.
Cream together the peanut butter, butter, and both sugars until smooth.
Add the milk and vanilla, stirring well to combine.
In a separate bowl, whisk together the flour, baking soda, and salt.
Combine the wet and dry ingredients, mixing until a soft dough forms.
Roll the dough into small balls (about an inch wide) and place them on the baking tray.
Use a fork to press a crisscross pattern on top of each cookie.
Bake for 10–12 minutes, or until the edges are golden brown.
Allow the cookies to cool on the tray for 5 minutes before transferring to a rack.
Store in an airtight container for up to a week (if they last that long!).