In a large mixing bowl, whisk together the flour, baking soda, baking powder, and salt until evenly combined. Set the dry ingredients aside.
Add the egg and vanilla extract, then beat on medium speed until fully incorporated and the mixture is smooth and well combined.
Gradually add the dry flour mixture to the wet ingredients. Mix on low speed (or by hand with a spatula) just until a thick, cohesive dough forms—avoid over mixing to keep the cookies tender.
When ready to bake, preheat your oven to 375°F and line baking sheets with parchment paper (or silicone baking mats) for easy release.
Remove one chilled dough disk from the refrigerator and unwrap it. On a lightly floured surface or pastry mat, roll the dough out to an even ⅛-inch thickness.Use a 3-inch rectangle cookie cutter to cut out 48 cookies.
Place 24 (half) of the 3-inch heart-shaped cookies (the solid bottoms) on the parchment-lined baking sheets, spacing them about 1 inch apart.
Take the remaining half of the cookies (the tops) and use a 1-inch heart-shaped cookie cutter to cut out the center of each one, creating a window. Gently remove the small cutout hearts and set them aside—these can be baked separately as adorable mini heart cookies!
Arrange the window cookies on the baking sheets as well.Bake in the preheated 375°F oven for 8–10 minutes, or until the edges are lightly golden brown. (The cookies will firm up as they cool, so avoid overbaking.)
Let the cookies cool on the baking sheet for 5 minutes, then carefully transfer them to a wire cooling rack to cool completely.
Repeat the rolling, cutting, and baking process with any remaining dough (re-chilling scraps if needed) until all cookies are baked and cooled.
While the Linzer heart cookies cool completely on the wire rack, prepare the jam buttercream filling.