Preheat oven to 350 degrees. Line two baking sheets with parchment paper. Make filling: With an electric mixer, beat cream cheese and butter until smooth. Add sugar and lemon juice; beat until combined. Cover; chill until firm, at least 30 minutes.
Meanwhile, make cookies: In a large bowl, whisk together butter, sugars, and egg yolk. In a medium bowl, whisk together flour, ginger, and salt. Add flour mixture to butter mixture; stir until combined. Mix in oats, carrots, and currants.
Drop dough by level tablespoons, 2 inches apart, onto prepared baking sheets. Flatten with the palm of your hand. Bake until edges are crisp, rotating baking sheets halfway through, 15 to 18 minutes. Transfer cookies to a wire rack to cool.
Turn half the cookies over, bottom side up; dollop each with about 1 teaspoon chilled cream-cheese filling. Top with remaining cookies, pressing gently to spread filling to edges. Serve immediately.
Before being filled, the cookies can be kept in an airtight container at room temperature for up to three days. The filling can be made ahead and chilled for up to five days.