For the cake: Preheat the oven to 350 degrees F.
Prepare the chocolate by melting it in the top of a double boiler, stirring until it is smooth. Add 1/4 cup (1/2 stick) of the butter and stir until it is melted and blended. Add the warm milk and stir until smooth. Set the chocolate aside to cool.
Line the bottoms only of three 9-inch cake pans with circles of parchment paper, or grease each pan bottom only with solid shortening and dust lightly with flour. Sift together the flour, baking soda and salt.
Whip the egg whites until stiff using the wire beater of the mixer. Transfer the beaten whites to a separate bowl and set aside.
In the mixer bowl, cream the remaining 1 1/2 sticks of butter and the sugar together until fluffy. Add the egg yolks one at a time, beating well after each addition. Add the melted, cooled chocolate and the vanilla. Mix well.
With the mixer on very low, stir in the flour mixture alternately with the buttermilk. Do this by adding about a third of the flour and slowly stirring it in completely. Then add about half the buttermilk and stir it in. Continue adding flour and buttermilk in this manner, ending with the flour. Scrape the sides and bottom of the bowl and stir again. With a long-handled spoon or spatula, fold and stir the beaten egg whites into the batter until the batter is smooth with no visible clumps of whites.
Divide the batter evenly between the prepared pans and bake for 30 to 40 minutes. Bake on the middle rack of the oven, allowing at least 1/4-inch clearance between the pans and the oven walls. The cake will rise above the pan edges as it bakes but will not spill over and will settle back down as it continues to bake. The cake is done when it begins to pull away from the sides of the pans and springs back to a light touch. Cool the layers in the pans for about 8 minutes.
Run a knife around the edges of each pan and turn the layers out onto wire racks that have been sprayed with cooking spray. Cool the layers completely before frosting.
For the frosting: Place the butterscotch morsels in a heatproof bowl set over a pan of simmering water or in the top of a double boiler. Stir until melted, then remove from the heat.
In an electric mixer fitted with the paddle attachment, cream the cream cheese until smooth. Add the butter and confectioner's sugar, and continue mixing. Add the melted butterscotch morsels and the heavy cream and vanilla, and mix until fully combined.
To assemble the cake: Place one layer on a cake stand and spread with frosting. Frost each layer completely, top and sides, as it is added to the cake.
Refrigerate the cake after it's frosted. Before serving, touch up any frosting that may have run down the sides.