For filling: In a spice grinder, process poppy seeds, 2 tablespoons (24 grams) granulated sugar, and salt until finely ground, 3 to 4 minutes.

In a small saucepan, heat milk and butter over medium heat until bubbles form around sides of pan. (Do not boil.)

In a medium bowl, whisk together egg yolk, lemon zest, and remaining 2 tablespoons (24 grams) granulated sugar. Slowly add hot milk mixture, whisking constantly. Return mixture to pan; cook over medium-low heat, whisking frequently, until thickened, 1 to 2 minutes. Strain mixture through a fine-mesh sieve into a medium bowl. Stir in poppy seed mixture. Cover with a piece of plastic wrap, pressing wrap directly onto surface of filling to prevent a skin from forming. Refrigerate until chilled, at least 1 hour.

For dough: In the bowl of a stand mixer fitted with the paddle attachment, beat butter, confectioners’ sugar, and lemon zest at medium speed until creamy, 3 to 4 minutes, stopping to scrape sides of bowl. Beat in egg and vanilla.

In a medium bowl, whisk together flour and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating until a smooth dough forms. Turn out dough, and press into a rectangle (about 1 inch thick). Wrap in plastic wrap, and refrigerate until firm, about 30 minutes.

Line 2 rimmed baking sheets with parchment paper.

On a lightly floured surface, roll dough to ¼-inch thickness. (If the dough is too stiff, let stand at room temperature for 15 minutes.) Using a 3¼-inch round cutter, cut dough, rerolling scraps as necessary. Spoon 2 teaspoons (10 grams) filling into center of each dough circle. Fold dough in from three sides, overlapping at corners, and pinch edges together to seal, leaving a small opening over filling. Place 2 inches apart on prepared pans. Refrigerate for 1 hour.

Preheat oven to 350°F (180°C).

Re-pinch corners of hamantaschen to ensure they’re well sealed.

Bake until bottoms and corners are golden, 20 to 25 minutes, rotating pans halfway through baking. Let cool completely on pans.