Preheat oven to 350°F. Line two baking sheets with parchment.
Cream softened butter, powdered sugar, and lemon zest until pale and fluffy.
Mix in vanilla and salt. Scrape the bowl.
Add flour in two additions. Mix just until a soft dough forms.
Chill dough 15 minutes to firm slightly for easier scooping.
Scoop 1-tablespoon portions, roll into balls, and set 2 inches apart. Gently flatten tops.
Bake 9–11 minutes, until edges look set and tops lose their shine. Cool 5 minutes on sheets, then rack-cool completely.
Beat cream cheese and butter until smooth and creamy.
Gradually beat in powdered sugar. Add lemon juice, zest, vanilla, and a pinch of salt; whip until fluffy.
Stir in a splash of cream if needed for spreadable consistency.
Pair similar-size cookies. Pipe or spread filling on half, cap with the rest, and twist gently to spread.
Chill sandwiches 10 minutes to set the cream before serving.