Lightly spoon flour into a dry measuring cup; level with a knife.
In a bowl, combine flour, brown sugar, and salt, stirring well with a whisk.
Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Press mixture firmly into a 13 x 9-inch baking dish coated with cooking spray.
Combine figs, water and 1/4 cup granulated sugar in a medium saucepan; bring to a boil over medium-high heat.
Cook 5 minutes or until figs are tender and sugar dissolves.
Cool slightly. Place fig mixture and juice in a blender; process until smooth.
Gently spread fig mixture over prepared crust.
Place remaining 1/4 cup granulated sugar, cheese, vanilla, and egg in a medium bowl; beat with a mixer at medium speed until smooth.
Pour over fig mixture; spread to edges. Bake at 350° for 30 minutes or until set and lightly browned.
Cool in pan on a wire rack; sprinkle with powdered sugar.