In a large bowl, beat eggs and egg yolks until slightly thickened. Gradually add sugar, beating until thick and lemon-colored. Combine flour and baking powder; gradually add to egg mixture with milk and butter, beating well after each addition. (Batter will be thick).
Spread evenly into a greased and floured 15-in. x 10-in. x 1-in. baking pan. Bake at 350° for 12-15 minutes or until a toothpick inserted near the center comes out clean.
Cool for 10 minutes before inverting onto a wire rack to cool completely. Cut a thin slice off each side of cake. Cut cake into 1-1/4-in. squares. Freeze cakes.
In a large saucepan, combine the sugar, water and cream of tartar. Bring to a boil, without stirring, until a candy thermometer reads 226°. Cool to 100°; beat in confectioners' sugar until smooth.
Keeping glaze warm, dip cake squares into glaze with a two-tine fork, allowing excess to drip off. Place on wire racks over waxed paper. Add hot water, 1 teaspoon at a time, if glaze becomes too thick. Let dry completely. Decorate with frosting and sprinkles. Yield: 70 petit fours.