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Lightly butter the bottom and sides of a 2-quart baking dish, 9" x 13" pan, or equivalent.
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Toss the bread cubes with 1 cup (170g) of the chopped semisweet chocolate, and place in the prepared pan.
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Combine the remaining 1/2 cup (85g) chopped chocolate with the sugar, cocoa, and 1 1/2 cups (340g) of the milk or half & half in a saucepan set over low heat.
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Cook, stirring, until the chocolate is melted and the mixture is thickened and smooth.
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Transfer to a large bowl, and whisk in the remaining 1 1/2 cups (340g) milk or half & half. Whisk in the eggs, salt, and vanilla.
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Pour the mixture over the bread cubes and let rest for 30 minutes or so at room temperature, until the chocolate custard has been absorbed by the bread.
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Preheat the oven to 325°F.
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Bake the pudding for 45 to 50 minutes, until it's set. Remove from the oven and let cool for 10 minutes to allow the custard to fully set before serving.
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Serve warm with whipped cream, ice cream, or dusted with confectioners' sugar.
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Store, refrigerated, for up to 5 days.