Step 1

Toast barley flour in a dry small skillet over medium-low heat, stirring constantly, until darkened slightly and nutty-smelling, about 4 minutes. Transfer to a medium bowl and whisk in all-purpose flour, salt, and baking powder.

Step 2

Using an electric mixer on medium-high speed, beat butter and granulated sugar until light and fluffy, about 4 minutes. Scrape in vanilla seeds (reserve pod for another use). Add egg and beat to incorporate, scraping down bowl as needed, about 1 minute. Reduce speed to low and add dry ingredients; beat until just combined. Divide dough in half and pat into disks; wrap tightly in plastic. Chill just until dough is easy to roll out and no longer sticky, 30–45 minutes.

Step 3

Working with one disk at a time, roll out dough between 2 sheets of parchment paper to ⅛" thick (dough will come nearly to the edges of parchment). If dough becomes too sticky, chill another 10–15 minutes. Stack sheets of dough, still sandwiched between parchment, and slide onto a baking sheet. Chill until very firm, at least 1 hour.

Step 4

Place racks in upper and lower thirds of oven; preheat to 350°. Unstack dough sheets and transfer to a surface; carefully peel away top sheet of parchment paper from each; reserve parchment. Punch out cookies as close together as possible with larger cutters. Punch out centers from half of cookies with smaller cutters; remove scraps. Re-cover cookies with reserved parchment paper and restack on baking sheet; freeze until firm, 10–15 minutes.

Step 5

Using a small offset spatula, divide half of cookies between 2 parchment-lined baking sheets, spacing 1" apart. Cover and chill remaining cookies while first batch bakes. Bake cookies, rotating baking sheets top to bottom and front to back halfway through, until pale golden brown and edges are set, 8–10 minutes. Let cool 5 minutes on baking sheets, then transfer to a wire rack and let cool completely. Repeat with remaining cookies.

Step 6

Spoon 1 tsp. apricot jam onto center of whole cookies. Dust cutout cookies with powdered sugar and place, sugar side up, on top of whole cookies so jam peeks through cutout.Do ahead: Dough can be rolled out 2 weeks ahead; stack, sandwiched between parchment, on a baking sheet, wrap in plastic, and freeze. Cookies can be assembled 5 days ahead; store airtight at room temperature.