In a stand mixer bowl, beat 1 cup (2 sticks) of room temperature unsalted butter until light and fluffy. Gradually add 1 cup of granulated sugar and continue mixing until well combined.
Mix in 2 large egg yolks, 1 teaspoon of lemon zest, and 1 teaspoon of vanilla extract until everything is thoroughly combined.
Add 2 cups of all-purpose flour to the mixture and blend just until the dough comes together.
Divide the dough into two equal parts, shape into round balls, and wrap them in plastic wrap. Refrigerate overnight to let them firm up.
Preheat your oven to 350°F (175°C). Roll out the chilled dough on a floured surface to prevent sticking.
Use a scalloped cookie cutter to shape your cookies. For half of them, use a smaller Linzer cutter to make a cutout in the center.
Place parchment paper on baking sheet. Place cookie tops and bottoms onto the sheet.
Line a baking sheet with parchment paper and place your cookie tops and bottoms on it. Bake for about 9 minutes, or until the edges are just lightly golden, keeping an eye on them as ovens may vary.
Move the baked cookies to a cooling rack. Once cool, spread a small dollop of your choice of jam on the bottom cookies. Gently press the top cookies with the cutout onto the jam-covered bottoms.
Dust the tops with powdered sugar if you'd like for a sweet finish.