Pre-heat the oven to 350ºF. Prepare a 13-inch x 9-inch baking dish by greasing it liberally with nonstick cooking spray. Tear off a sheet of aluminum foil that is about 1 1/2-times wider than the pan and press it down into the pan, letting the long edges overlap (this will make it easier to remove the bars from the pan later). Grease the foil with nonstick cooking spray and set the pan aside.
In a large mixing bowl, whisk together the flour, salt, baking powder, and spices. In a medium size mixing bowl, whisk together the melted butter, brown sugar, molasses, eggs, and vanilla. Add the wet ingredients to the dry and stir just to combine. Spread the batter into an even layer in the bottom of the prepared baking dish and set aside.
In a large mixing bowl, whip the cream cheese with a handheld mixer on medium speed until smooth and fluffy, about 1 minute. Add the egg and vanilla to the cream cheese and combine. Slowly stream the sweetened condensed milk into the cream cheese, mixing constantly until combined. Pour the cream cheese mixture into the baking dish, spreading it evenly over the gingerbread base.
Bake until the cheesecake layer is set and very light golden brown, 55-60 minutes. Cool completely and then chill for at least 2 hours. Using the foil overhang as a set of handles, lift the bars out of the pan and slice. Store the bars in an airtight container in the refrigerator for up to 5 days.
OPTIONAL GARNISHES: If you’d like to dress up these bars, garnish them with 1/4 cup finely chopped crystallized ginger or 1/4 cup crushed ginger snap cookies before baking.