Step 1

Heat butter in a large saucepan over medium, stirring occasionally, until butter is lightly browned and smells nutty, 6 to 8 minutes. Transfer butter to the bowl of a stand mixer; let cool completely, about 1 hour and 30 minutes.

Step 2

Stir together flour, salt, baking powder, cardamom, and ginger in a medium bowl; set aside.

Step 3

Split vanilla bean lengthwise, and scrape seeds into butter. Add brown sugar, and beat on medium-high speed until light and fluffy, about 5 minutes. Add egg, and beat until fully incorporated. Add yolks, and beat until fully incorporated. Reduce speed to low, and add flour mixture in 3 additions, beating well after each addition.

Step 4

Turn dough out onto a work surface, and knead to make sure all ingredients are incorporated, 1 to 2 minutes. Divide dough in half, and shape each portion into a disk. Wrap each disk in plastic wrap, and chill until firm, about 2 hours or up to overnight.

Step 5

Preheat oven to 350°F. Remove 1 dough disk from refrigerator, and let stand at room temperature to soften slightly, about 20 minutes. Unwrap dough, and roll between 2 sheets of parchment paper to about 1/8-inch thickness. Using a 2-inch round cutter, cut out cookies, and transfer to parchment paper–lined baking sheets, leaving about 1 inch between cookies. Gather scraps once, reroll, and cut out more cookies. (Refrigerate rerolled dough before cutting if it becomes too soft.) Repeat softening, rolling, and cutting with remaining dough disk, making sure to cut the same number of cookies you cut from the first disk. Using a 1-inch cutter, cut the centers out of half of the cookies. Bake in preheated oven until golden brown around edges, about 10 minutes. Let cookies cool on baking sheets about 30 minutes.

Step 6

Dust cutout cookies with powdered sugar. Flip remaining cookies over, and spread each with about 1 teaspoon jam. Sandwich with cutout cookies.