Heat oven to 350 degrees F. Coat 2 large baking sheets with cooking spray.
In medium-size bowl, mix flour, baking soda and salt. In large bowl, beat peanut butter and butter until smooth, 2 minutes. Add sugars; beat 2 minutes. Beat in egg, milk and vanilla. On low, beat in flour mixture.
For each cookie, roll scant tablespoon of dough into a ball; place balls on sheets, 2 inches apart. With fork, flatten each ball in crosshatch pattern into 2-inch round.
Bake until colored around edges, 12 to 14 minutes, rotating sheets halfway through. Let cool on sheets 1 minute. Transfer to rack; let cool. Makes 42 cookies.
