To prepare cookies, weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, 1/2 teaspoon salt, and baking powder, stirring with a whisk. Place powdered sugar and butter in a large bowl. Beat with a mixer at medium-high speed until well blended. Add 2 tablespoons milk and vanilla; beat 1 minute or until well combined. Add the flour mixture; beat on low speed until just combined.
Shape the dough into a 6-inch disk. Cover tightly with plastic wrap; chill 30 minutes. Discard plastic. Roll dough to a 1/4-inch thickness on a lightly floured surface. Cut out 36 (2-inch) round cookies, rerolling scraps as necessary. Using a small decorative cookie cutter, cut a cat-shaped opening in 18 rounds. Place cookies 1 inch apart on baking sheets lined with parchment paper. Bake at 350° for 14 minutes or until lightly browned. Cool on a wire rack.
To prepare filling, combine chocolate and 2 tablespoons milk in a microwave-safe dish; microwave at HIGH for 1 minute or until melted, stirring every 15 seconds. Stir just until smooth. Combine 1/2 cup powdered sugar, cocoa, and dash of salt in a bowl, stirring well with a whisk. Add chocolate mixture to sugar mixture; stir just until smooth. (Mixture will thicken as it cools.) Divide chocolate mixture evenly among 18 whole cookies; spread in a thin, even layer. Top each cookie with a cut-out cookie.