1. Heat oven to 375 degrees . Line 2 or 3 large baking sheets with nonstick foil.
2. Cookies. In medium-size bowl, whisk flour, cocoa, baking powder and salt. In a large bowl, beat together the butter and sugar until smooth. Beat in eggs, one at a time, beating well after each, until mixture is a pale yellow color. On low speed, beat in half of the flour mixture. Beat in milk and vanilla and then remaining flour mixture.
3. Drop dough by level tablespoonfuls onto prepared sheets, spacing at least 1 1/2 inches apart, spreading slightly to a 2-inch round (about 48 rounds total). Bake at 375 degrees for 12 to 13 minutes or until tops are dry. Cool completely.
4. Meanwhile, prepare Filling. In a medium-size bowl, beat together confectioners' sugar, butter, 2 tablespoons water, vanilla and food coloring until smooth and desired color. Once cookies are cool, sandwich together (flat side to flat side) with a scant tablespoon of filling. Store in airtight container.