Preheat oven to 350 ?F. Grease and line a 9-inch square pan with parchment so that it hangs over the sides.
For base, stir melted butter and sugar to blend. Stir in egg, then cookie crumbs and coconut. Press into bottom of prepared pan and bake for 12 minutes. While still warm, sprinkle base with toffee bits. Cool completely.
For filling, stir all ingredients, except marshmallows in a bowl over gently simmering water, until melted. Take off the heat and stir in marshmallows. Pour over cooled crust and chill for 2 hours or freeze for 30 minutes.
For topping, melt chocolates separately and then use a piping bag or spoon to drizzle over for a topping. Chill at least an hour before slicing.