Stir together 1 1/3 cups flour and brown sugar in a small bowl. Cut butter into flour mixture with a pastry blender or fork until crumbly; stir in pecans. Set aside.
Beat cream cheese at medium speed with an electric mixer until smooth; add granulated sugar and 1 tablespoon flour, beating until blended. Add egg and 1/2 teaspoon vanilla, beating until blended.
Melt semisweet chocolate morsels in a microwave-safe bowl at HIGH for 30-second intervals until melted (about 1 1/2 minutes total time). Stir until smooth.
Beat butter and brown sugar at medium speed with an electric mixer, beating about 5 minutes or until well blended. Add eggs, 1 at a time, beating just until blended after each addition. Add melted chocolate, beating just until blended.
Sift together flour, baking soda, and salt. Gradually add to chocolate mixture alternately with sour cream, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Gradually add 1 cup hot water in a slow, steady stream, beating at low speed just until blended. Stir in vanilla.
Spoon Chocolate Velvet Cake Batter evenly into 2 greased and floured 9-inch springform pans. Dollop cream cheese mixture evenly over cake batter, and gently swirl through cake batter with a knife. Sprinkle reserved pecan mixture evenly over cake batter.
Bake at 350° for 45 minutes or until set. Cool on a wire rack.
Whisk together powdered sugar, milk, and remaining 1/2 teaspoon vanilla extract. Drizzle evenly over tops of coffee cakes.