In a small heavy saucepan, whisk lemon zest and sugar; let sit 1–2 minutes.

Whisk in egg and yolk, then add lemon juice.

Cook over medium-low heat, whisking constantly, 5–8 minutes until thickened (coats a spoon, about 170–175°F).

Remove from heat, stir in butter until smooth. Strain if desired for silky texture.

Press plastic wrap on surface and chill 1–2 hours.

Beat butter and sugar until creamy (about 90 seconds).

Add egg, lemon emulsion, and vanilla; mix until smooth.

Whisk dry ingredients together, then stir into wet just until dough forms.

Scoop 1-tablespoon portions, roll into balls, and place 1 inch apart on lined baking sheets.

Preheat oven to 350°F.

Press a deep well in each ball with the back of a 1-tsp measuring spoon (pinch any cracks closed).

Fill each well with ~1 tsp lemon curd or jam.

Bake 10–12 minutes until edges are lightly golden.

Cool on sheet 5 minutes, then transfer to wire rack to cool completely.

Whisk powdered sugar with 2 tbsp lemon juice until smooth. Add more juice until drizzlable. Stir in zest, salt, and vanilla.

Drizzle over completely cooled cookies using a fork or spoon.

Let glaze set 30–60 minutes before serving.