In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium speed until creamy, 2 to 3 minutes, stopping occasionally to scrape sides of bowl. Add egg, beating until well combined. Beat in zest and vanilla.
In a medium bowl, whisk together flour, salt, baking powder, and cardamom. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined.
Transfer a portion of dough to a cookie press fitted with a daisy-shape disk. Press dough ½ inch apart on 3 ungreased baking sheets. (Do not use parchment paper.) Repeat with remaining dough.
Bake for 4 minutes. Remove from oven; using the handle of a wooden spoon, gently make a slight indentation in center of each cookie. Top each with about ¼ teaspoon jam. Bake until cookies are set and bottoms are lightly golden, about 7 minutes more. Let cool on pans for 2 minutes. Using a small of set spatula, gently loosen cookies from pans and transfer to a wire rack; let cool completely.
Notes
*We used Smucker's Red Plum Jam and Apricot Preserves.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/jam-filled-butter-cookie-blossoms/