Make Orange-Scented Custard Sauce and refrigerate.
Preheat oven to 400°F.
Heat oil and butter over low heat in a small saucepan just until butter melts. Brush both sides of the bread slices with butter mixture and place on a baking sheet. Bake until golden brown, 5 to 7 minutes per side.
Overlap toasted bread slices in an ungreased 9-inch square baking dish. Reduce oven temperature to 325 degrees .
Whisk cocoa and salt in a medium saucepan. Gradually whisk in milk. Bring to a bare simmer over low heat. Remove from heat, add chocolate and whisk until it melts.
Whisk eggs, brown sugar and vanilla in a medium bowl until blended. Gradually whisk hot chocolate mixture into egg mixture. Pour custard over bread in baking dish. Let stand for 15 minutes. Meanwhile, boil water for the water bath.
Set baking dish in a roasting pan and place in the oven. Add boiling water to the roasting pan to reach halfway up sides of baking dish. Bake pudding until just set, 20 to 25 minutes. (It should still jiggle slightly in the center.) Remove baking dish from roasting pan and cool on a wire rack for about 20 minutes. Serve warm with Orange-Scented Custard Sauce.