Preheat oven to 180 C / Gas 4. Grease and flour a 20x30cm baking dish.
In a large bowl, cream together the butter and sugar. Beat in the eggs, one at a time, then stir in 1 1/2 teaspoons vanilla. Combine the flour, cream of tartar and cocoa; stir into the egg mixture until well blended. Fold in walnuts. Spread half of this mixture into the bottom of the prepared tin.
Make the middle layer. In a medium bowl, stir together the coconut, sweetened condensed milk and 1 tablespoon vanilla. Carefully layer this over the chocolate layer in the tin. Top with the remaining chocolate batter. Spread to cover evenly.
Bake for 45 to 50 minutes in the preheated oven, until top is no longer shiny. Cool in the tin before cutting into bars.