Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
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.
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.