Preheat oven to 350 degrees. Coat a 17-by-12-inch baking sheet with cooking spray and line the bottom with parchment leaving a 1-inch overhang. Whisk together flour, baking soda, salt, and spices.
In the bowl of an electric mixer, beat butter and brown and granulated sugars on medium-high speed until light and fluffy. Add eggs and yolk, 1 at a time, beating well after each addition and scraping down sides of bowl as needed. Beat in vanilla and molasses and then reduce speed to low. Gradually add flour mixture, and beat until combined.
Spread batter into prepared pan and set aside.
In a small bowl, beat the cream cheese, eggs, sugar, lemon zest, juice and vanilla until smooth. Fill a pastry bag without a tip, or a ziplock bag with the corner cut off, with the filling and pipe it onto the batter in ribbons lengthwise approximately 1 1/2 inches apart. Cut through the filling with a knife widthwise, alternating directions, to create the swirl.
Bake until edges are golden, about 25 minutes. Let cool completely in pan on a wire rack. Cut into 2-inch squares.