Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13 baking dish.
Slice baguette in 1/4 inch slices and brush one side with melted butter. Place on a baking sheet and into preheated oven until golden, about 1 minute.
Melt chocolate chips in microwave or double boiler. Set aside.
In a medium saucepan over low heat, heat cream and milk until warm. Do not scald.
In a large bowl beat eggs, egg yolks, 1/2 cup sugar and 1 tablespoon vanilla until smooth. Blend in warm cream mixture a little at a time. Whisk egg mixture into melted chocolate until smooth.
Arrange toasted bread slices, buttered side up, in prepared dish until dish is full. Pour chocolate mixture over bread and let rest 40 minutes, until liquid is absorbed.
Line a roasting pan with a damp kitchen towel. Place baking dish on towel, inside roasting pan, and place roasting pan on oven rack. Fill roasting pan with boiling water to reach halfway up the sides of the baking dish. Bake 40 to 50 minutes, until knife inserted in center comes out clean. Let rest 8 hours or overnight.
To make sauce, melt unsweetened chocolate in small saucepan over low heat. Stir in 1 tablespoon butter until melted. Stir in boiling water, 1/2 cup sugar and corn syrup until smooth. Increase heat to medium and bring to a boil Boil gently 3 minutes. Remove from heat and stir in 1 teaspoon vanilla.
To serve: Warm bottom of baking dish, loosen edges of pudding with a knife then invert cold pudding onto a serving platter. Serve with warm chocolate sauce.
