Heat oven to 375 degrees F. Line baking sheets with aluminum foil; coat with cooking spray.
Mix flour, baking powder, baking soda and salt in bowl. Beat butter and sugar in second bowl until creamy, 1 minute. Beat in vanilla and eggs; beat 30 seconds. On low speed, beat in cocoa. Alternately beat in flour mixture and milk in 3 additions.
Drop 2 tablespoons mixture per cookie onto prepared sheets, spacing 3 inches apart. Shape each into 2-1/4-inch rounds (keep size equal since they will be sandwiched.)
Bake in 375 degree F oven for 12 to 14 minutes or until cookies spring back when lightly touched in center. Cool on sheets 5 minutes. Remove cookies to rack to cool completely.
Stir flour and milk in saucepan until smooth. Bring to simmering over medium heat, whisking, until thickened and bubbly; cook 1 minute.
Remove from heat. Whisk in 2 tablespoons butter until smooth. Press waxed paper directly on surface. Let stand until cool to touch, about 45 minutes.
Beat remaining 6 tablespoons butter, the vanilla and confectioners sugar in small bowl until smooth, about 1 minute, scraping bottom and side of bowl as needed. Add milk mixture; beat 1 minute or until smooth and fluffy.
Sandwich together pairs of cookies with 2 tablespoons filling, pressing lightly until filling begins to show around edges. Store between sheets of waxed paper in airtight containers in refrigerator up to 3 days or in freezer up to 1 month. Makes 15 pies.