Cookies: In medium bowl, whisk together flour, cornstarch, baking powder and salt.
In large bowl, using handheld electric mixer, beat together butter and sugar until light and fluffy. Beat in egg and vanilla until incorporated.
On low speed, beat in flour mixture just until combined. Do not overbeat, remove from bowl. Divide dough in half and shape each half into a disk. Wrap each disk with plastic wrap and chill for 45 to 60 minutes or until dough is chilled and firm.
Preheat oven to 350°F (180°C). Working with one portion at a time, roll dough on lightly floured work surface to 1/4-inch (0.5 cm) thickness (if dough is too hard to roll, let stand at room temperature for 5 to 10 minutes).
Using 2 1/2-inch (6 cm) round cookie cutter, cut out 44 to 48 rounds, rerolling scraps as needed. Using 1-inch (2.5 cm) holiday-themed cookie cutter, cut out a window in centre of half the cookies. (Bake cutout cookies or reroll.) Transfer cookies to parchment paper–lined baking sheet, spacing about 2 inches (5 cm) apart. Freeze for 10 minutes.
Bake cookies for 10 to 14 minutes or until edges are lightly golden and bottoms are set. Let cool on pan for 5 minutes, then transfer to wire rack to cool completely.
Glaze: In bowl, whisk together confectioners’ sugar, milk, honey or maple syrup and vanilla until smooth.
Dip window cookies in glaze to coat one side, letting excess drip back into bowl. Arrange on parchment paper–lined sheet and let stand for 1 to 2 hours or until hardened and set. Spoon 1/2 tsp (2 mL) jam on remaining cookies, spreading slightly; place glazed cookie on top. Repeat assembly until complete.