To prepare filling: In a bowl of an electric mixer on medium speed, combine poppyseeds, walnuts, honey, egg, butter and corn syrup and mix until creamy, about 5 minutes.
To prepare cookies: When ready to bake, preheat oven to 350 degrees and line baking sheets with parchment paper. On a lightly floured work surface, using a lightly floured rolling pin, roll dough to a 1/4-inch thickness. Using a 2- to 3-inch round cookie cutter or drinking glass, cut circles from dough. Place about 2 teaspoons filling into the middle of each circle. Fold two edges of circle to meet in the middle, forming a kolache shape. Place filled cookies 2 inches apart on prepared baking sheets and bake until slightly browned, about 10 to 12 minutes. Remove from oven and cool 2 minutes before transferring cookies to a wire rack to cool completely.
To prepare glaze: In a small bowl, whisk together powdered sugar and lemon juice until smooth, adding more lemon juice if necessary for desired consistency and tartness. Drizzle icing over cooled cookies.