Heat oven to 350°F; spray bottom of 3 (9 inch) round pans with cooking spray. Line bottoms with parchment paper; spray paper. Sprinkle bottoms and sides of pans with flour, tapping out excess.
Whisk water and cocoa in medium bowl until smooth. Whisk in buttermilk and 1 tbsp vanilla. Whisk flour, baking soda and salt in a large bowl.
Beat 3 cups brown sugar and 1 1/2 cups butter in large bowl at medium speed 4 to 5 minutes or until light and creamy. Add eggs one at a time, beating well after each addition. At low speed, beat in flour mixture alternatively with chocolate mixture just until blended, beginning and ending with flour mixture. Divide batter between pans; smooth tops with spatula.
Bake 25 to 30 minutes or until toothpick inserted in the center comes out clean and cakes just begin to pull away from the sides of pans, rotating pans during last 5 minutes of baking if necessary. Cool in pans on wire rack 15 minutes. Invert cakes onto wire rack, remove parchment. Cool completely.
Beat cream cheese and 1 cup butter in large bowl at medium speed 3 to 4 minutes or until smooth and creamy. Beat in powdered sugar and 1 1/4 cups brown sugar until well blended. Beat in 1 1/2 tsp vanilla.
Put 1 cake layer, top-side up, on platter; spread with about 1 cup of frosting. Top with second cake layer; spread with one cup of frosting. Top with remaining cake layer; frost top and sides of cake with thin layer of frosting.
Refrigerate 15 minutes. Frost top and sides of cake with remaining frosting. Refrigerate until ready to serve. (Cake can be made 1 day ahead. Cover and refrigerate).