Using an electric mixer on medium-high speed, beat ¾ cup (1½ sticks) unsalted butter, preferably cultured, room temperature, ½ cup (100 g) granulated sugar, 1 tsp. finely grated lemon zest, 1 tsp. vanilla bean paste or vanilla extract, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a large bowl until light and fluffy, about 3 minutes.

Add 1 large egg yolk and beat until incorporated, about 1 minute.

Add 2 cups (250 g) all-purpose flour and beat on low speed until no dry streaks remain (be careful not to overmix).

Turn dough out onto a surface and knead gently to bring together into a ball.

Split dough in half (about 270 g each). Using your hands, roll each into a 10x1½" log (dough should be easy to handle; dust surface very lightly with flour if dough feels sticky).

Place logs 3" apart on a large parchment-lined baking sheet.

Run your index finger or the round handle of a large wooden spoon down the entire length of each log through the center to create a deep channel (you want to push dough down as far as possible without tearing; logs will lengthen to about 12").

Chill logs in freezer until firm, about 30 minutes.

Meanwhile, place a rack in middle of oven; preheat to 350°.

Remove logs from freezer, spoon about 3 Tbsp. raspberry or apricot jam along channel in each log.

Bake logs until dough is set and golden brown underneath, 18–20 minutes.

Let cool on baking sheet.

Using a small knife, slice logs crosswise on a deep diagonal into 1"-wide pieces.

Whisk ⅓ cup (37 g) powdered sugar, 2 tsp. fresh lemon juice, and a large pinch of kosher salt in a small bowl until smooth.

Glaze should be thick but pourable; adjust consistency with more powdered sugar or lemon juice if needed.

Drizzle glaze over logs; let sit until glaze is set, at least 30 minutes.

Do ahead: Cookies can be baked 2 days ahead. Store, loosely covered, at room temperature.