Prepare the Lemon Cream Filling: Combine softened cream cheese, powdered sugar, lemon zest, and lemon juice in a mixing bowl. Beat until completely smooth with no lumps. Line a plate with parchment paper and drop 23 heaping teaspoon-sized portions onto the paper. Place in freezer for at least 1 hour until completely solid.
Prepare the Cookie Dough: In a large bowl, cream together the softened butter, brown sugar, granulated sugar, and lemon zest until light and fluffy (about 3 minutes). Add the egg, vanilla extract, and lemon juice, mixing until well incorporated.
Add Dry Ingredients: In a separate bowl, whisk together the flour, salt, and baking soda. Gradually add this dry mixture to the wet ingredients, mixing just until combined. Be careful not to overmix.
Preheat and Prepare: Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper. Place the graham cracker crumbs in a shallow bowl.
Form Cookie Balls: Scoop approximately 2 tablespoons of cookie dough and roll into a ball. Make an indentation in the center with your thumb.
Add Filling: Remove the frozen lemon cream cheese portions from the freezer. Place one frozen cream cheese portion into the indentation of each cookie dough ball.
Seal and Coat: Gently wrap the cookie dough around the cream cheese filling, ensuring it's completely enclosed. Roll each filled cookie ball in the graham cracker crumbs until fully coated. Place a few larger graham cracker pieces on top for decoration.
Shape and Bake: Slightly flatten each cookie and place on the prepared baking sheet, spacing them about 2 inches apart. While one batch bakes, refrigerate the remaining dough balls to keep them firm.
Bake: Bake for 10-12 minutes, or until the edges are set and just beginning to turn golden. The centers will still look slightly underdone.
Cool: Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.