Position a rack in the center of the oven and heat the oven to 350 degrees F. Line three baking sheets with parchment.

In a medium bowl, whisk the flour, ginger, cinnamon, cardamom, baking soda, and salt.

In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and both sugars on medium-high speed until light and fluffy, about 3 minutes. Add the molasses, egg, and vanilla and continue to beat until incorporated, about 1 minute. Reduce the speed to low, slowly add the flour mixture, and mix until just incorporated, about 1 minute. Shape the dough into a disk, wrap in plastic, and refrigerate until firm, about 1 hour.

Put about 1/3 cup granulated sugar in a small bowl. Using your hands, roll teaspoonfuls of dough into 1-inch balls. Roll each ball in sugar and arrange them about 2 inches apart on the lined baking sheets. Use the bottom of a glass to flatten the cookies slightly. Bake one sheet at a time until the cookies feel dry to the touch and are beginning to firm up (they'll still feel soft inside), 10 to 14 minutes. Cool completely on racks.

With a hand mixer, mix the cream cheese and lemon zest in a medium bowl until smooth. Slowly add the confectioners' sugar and continue to mix until smooth.

Drop about 1 teaspoon of the lemon cream in the center of a cookie, top with another cookie, and gently press them. Repeat with the remaining cookies. Store in an airtight container for up to 2 days.