Preheat the oven to 350 degrees F (175 degrees C). Butter a 9x13-inch baking pan.
Combine flour, sugar, and salt in a large bowl. Cut in butter using a pastry cutter or fork until mixture resembles coarse crumbs. Stir in 1 egg until mixture is evenly combined but still crumbly. Firmly press 1/2 of the mixture into the bottom of the prepared pan to form an even crust.
Beat cream cheese, sugar, egg, maple syrup, and vanilla extract in a bowl until creamy. Spread mixture evenly over the crust. Drop spoonfuls of cranberry sauce on top until evenly distributed. Crumble the remaining crust mixture on top.
Bake in the preheated oven until top is lightly browned and cream cheese is set, 45 to 60 minutes. Let cool before cutting into bars, at least 30 minutes.