In a mixer bowl fitted with the paddle attachment, beat butter and sugar on medium speed for about 3 minutes, until light and fluffy. Add peanut butter and beat until combined. Beat in egg, vanilla extract, and milk. Scrape down the sides and bottom of the bowl as needed. Add flour in two additions and beat on low speed just until combined. Then add peanut butter chips. Do not overmix.
Preheat oven to 350°F/180°C. Line 2 pans with parchment paper.
Drop rounded balls of dough (57g/each or about 2-3 tablespoons), onto prepared baking sheet, leaving 2-inches/5cm between them. Bake for 12-14 minutes, until cookies are puffy and begin to brown at the edges. Cookies will appear undone but will continue to bake on the warm baking sheet. Leave cookies to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.