Start by cooking the strawberry jam in a small pot over medium heat, stirring occasionally, until it thickens and reduces slightly, about 7-10 minutes. Transfer to a bowl and let cool to room temperature (about 1 hour)—this can be done while you prepare and chill the dough. While the jam cools, whisk together the flour, baking powder, and salt in a separate bowl to evenly distribute the leavening agent. This step sets you up for efficient assembly later and ensures your jam won't melt the cookies when assembled.
Beat the softened butter and sifted confectioners' sugar together for about 3 minutes until the mixture is light and fluffy—this incorporates air and creates a tender cookie texture. Add the eggs and vanilla extract, beating until fully combined and the mixture looks smooth and pale. Gradually add the dry ingredient mixture from Step 1, mixing on low speed until just combined; be careful not to overmix, which can develop gluten and make the cookies tough. Once the dough comes together, divide it in half and shape each portion into a flat disk.
Wrap both dough disks and refrigerate for at least 1 hour—this prevents spreading during baking and makes the dough easier to work with. About 15 minutes before you're ready to bake, preheat your oven to 375°F and line two baking sheets with parchment paper. Remove the first dough disk from the refrigerator and let it sit for about 10 minutes at room temperature to soften slightly, making it easier to roll without cracking.
On a lightly floured surface, roll the first dough disk to about 1/6 inch thickness. Using a 2-inch round cutter, cut out as many rounds as possible and place them on one of your prepared baking sheets, spacing them about 1 inch apart. Bake for 7 minutes until the edges are just set and the bottoms are lightly golden—these will be your solid base cookies. Transfer to a cooling rack after a quick 5-minute rest on the baking sheet.
While the first batch cools, roll the second dough disk to the same 1/6 inch thickness and cut out 2-inch rounds, placing them on the second baking sheet. Here's where I like to add a personal touch: use a smaller round cutter (about 1/2 inch) to cut out the centers of these cookies, creating windows for the jam to show through. Bake these cutout cookies for 7-10 minutes—they may take slightly longer since they're thinner in some spots—until the edges are set and the bottoms are lightly golden. Cool for 5 minutes on the sheet, then transfer to the cooling rack.
Once all cookies have cooled completely, spread about 1 teaspoon of the cooled jam from Step 1 onto the flat side of each solid cookie—I like to use a small offset spatula or the back of a spoon for even distribution. Top each jam-topped cookie with a cutout cookie, pressing gently so the jam peeks through the center hole. Just before serving, dust the finished cookies generously with fresh confectioners' sugar, which creates that beautiful, delicate appearance linzer cookies are known for.
