Preheat the oven to 350 F and line 2 baking sheets with parchment paper.
Beat the peanut butter, butter, brown sugar and granulated sugar for 2 minutes until creamy, then beat in the milk and vanilla.
Whisk the flour, baking soda and salt, then mix into the wet ingredients until a soft dough forms.
Roll into 1 1/2 tablespoon balls, place on the sheets and press a crosshatch pattern into each with a fork.
Bake for 10 to 12 minutes, until the edges are lightly golden and the centers still look soft.
Cool on the pan for 5 minutes, then move to a rack. The cookies firm up soft and chewy as they cool.
