Cream the butter, cream cheese, and sugar together until light and fluffy, about 2 minutes. Mix in the egg yolk, vanilla extract, and lemon zest. Gradually add the flour and salt while mixing on low speed until just combined.

Split the dough into two pieces and shape each into a disc. Roll each disc between two lightly floured pieces of parchment paper until about 1/4-inch thick. Refrigerate for at least 1 hour.

Preheat oven to 350°F (175°C). Use a 2-inch round cookie cutter to cut out rounds from the chilled dough. Place on ungreased baking sheets, spaced 1 inch apart. Bake for 4 minutes, rotate sheets, and bake until edges are lightly golden, about 2 to 4 more minutes.

Cool cookies on the sheet for 5 minutes before transferring to a wire rack to cool completely.

Simmer lemon juice over medium-high heat until reduced to about 3/4 cup. Stir in lemon zest and let cool to room temperature.

Whisk together egg, egg yolks, and sugar. Slowly add cooled lemon juice and zest mixture while whisking continuously.

Return mixture to saucepan and cook over medium heat, stirring constantly, until thickened to pudding-like texture, about 6 to 8 minutes.

Strain mixture through a fine-mesh strainer to remove zest or bits of cooked egg. Add cubed butter and a pinch of salt while still warm, stirring until smooth. Let cool completely.

Take half of the cooled cookies and flip them upside down. Place 1 heaping teaspoon of lemon curd in the center of each. Cover with remaining cookies and press down gently to create a sandwich.