Methods

For cake:
Preheat oven to 350°F. Spray three 9-inch-diameter cake pans with 1 1/2-inch-high sides with nonstick spray. Line bottom of pans with parchment paper. Whisk flour and next 4 ingredients in medium bowl. Using electric mixer, beat brown sugar and butter in large bowl until fluffy, about 2 minutes. Add eggs 1 at a time, beating well after each addition. Beat in vanilla. Beat in dry ingredients in 3 additions alternately with buttermilk in 2 additions. Beat in 1/2 cup lukewarm water. Stir in chocolate chips.

Divide batter among prepared pans (about 2 1/3 cups for each). Smooth tops. Bake cakes until tester inserted into center of cakes comes out clean, about 22 minutes. Cool completely in pans on racks. Invert cakes onto 9-inch-diameter cardboard rounds or tart pan bottoms (cakes are delicate). Peel off parchment.

For frosting:
Combine milk chocolate and bittersweet chocolate in large bowl. Stir sugar and 1/2 cup water in medium saucepan over medium heat until sugar dissolves. Boil without stirring until syrup is deep amber color, occasionally brushing down sides of pan with wet pastry brush and swirling pan, about 10 minutes. Carefully and slowly add whipping cream (mixture will bubble vigorously). Stir over low heat until any hard caramel bits dissolve and mixture is smooth. Pour caramel over chocolate; let stand 1 minute to allow chocolate to soften, then whisk until chocolate is melted and smooth. Chill chocolate-caramel frosting until completely cool, about 2 hours. Let stand 1 hour at room temperature before continuing.

Using electric mixer, beat frosting just until color resembles milk chocolate and frosting is easily spreadable, about 1 minute (do not overbeat or frosting will become stiff and grainy). If necessary to correct graininess, set bowl with frosting over saucepan of simmering water for 10-second intervals, whisking just until frosting is smooth and spreadable.

Place 1 cake layer on platter, flat side up. Spread 1 cup frosting evenly over top. Top with second cake layer, flat side up, pressing slightly to adhere. Spread 1 cup frosting over top. Top with third cake layer, rounded side up, pressing slightly. Spread remaining frosting over top and sides of cake, swirling decoratively. (Can be made 2 days ahead. Cover with cake dome and store at room temperature.)