Preheat oven to 350 degrees. In a large bowl, using an electric mixer on high speed, beat butter, confectioners' sugar, lemon zest, and salt, until combined. With mixer on low, add flour 9dough will still be stiff); finish mixing with a wooden spoon.
Turn dough out onto a piece of plastic wrap, pat into a disk about 1/4 inch thick. Wrap, and chill until firm, about 1 hour (and up to 3 days).
Unwrap dough; place on a lightly floured piece of parchment or waxed paper. With a lightly floured rolling pin, roll dough about 1/8 inch thick (if dough cracks, let it warm up slightly).
Cut out cookies with a 1 1/2-inch round cutter (re-roll scraps once, chilling of too soft). Place 1 inch apart on two baking sheets; sprinkle with granulated sugar. Bake until barely beginning to brown, 15 to 20 minutes; transfer to wire racks to cool completely.
Form sandwiches: Place about 1 teaspoon Creamy Lemon Filling between two cookies, sugared sides facing out; squeeze gently.
Creamy Lemon Filling: In a small bowl, mix cream cheese and zest until smooth. Gradually add 1 cup confectioners' sugar, missing until smooth. Mix in remaining sugar as necessary to create a firm but spreadable filling.
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