Place dough in a medium bowl. Add finely chopped white baking pieces and 1 tablespoon poppy seeds; stir to combine. Working between sheets of parchment paper or waxed paper, roll the dough out to 1/4-inch thickness. Slide onto a cookie sheet and freeze at least 1 hour or chill at least 3 hours.
Preheat oven to 350 degrees F. Line cookie sheets with parchment paper; set aside.
Peel the paper from the top of the dough. Use a 2-inch round cutter to cut circles from dough (if dough is too firm, let stand a few minutes before cutting). Arrange 1 1/2 inches apart on prepared cookie sheets. Gather scraps, roll, and chill as above.
Bake for 14 to 16 minutes or until golden around the edge and on the bottom. Cool on cookie sheets for 5 minutes. Remove and cool on wire racks.
Spread tops of cooled cookies with melted white chocolate baking pieces. Sprinkle with 1/4 teaspoon poppy seeds. Chill about 30 minutes or until chocolate sets.
Vanilla Cookie Dough Base
In a very large mixing bowl beat butter with an electric mixer on medium to high speed 30 seconds. Add sugar and salt; beat on medium speed 3 minutes or until smooth and creamy. Add egg whites and vanilla; beat until combined. Gradually add flour, beating until combined.