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1
Heat butter in a small skillet, preferably nonstick, over medium-low until it begins to foam. Add brioche and cook, turning occasionally, until golden brown on all sides, about 3 minutes total. Transfer to paper towels and let drain.
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2
Wipe out skillet and sprinkle with sugar and salt; set over medium heat. Cook (undisturbed) until edges of sugar begin to melt, about 1 minute. Stir sugar, bringing edges in toward the center to prevent burned spots, and continue cooking until all sugar is melted and turns amber color, about 4 minutes. Add brioche and quickly turn to coat all sides in caramel, about 30 seconds. Transfer to a parchment-lined rimmed baking sheet and let cool.
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3
Combine milk and cream in a 2-cup measuring glass. Pour 1/4 cup milk mixture into a small saucepan and add bittersweet chocolate and milk chocolate. Heat over medium-low, stirring occasionally, until chocolate is melted, about 2 minutes. Reserve remaining milk mixture.
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4
Meanwhile, whisk cornstarch and 2 Tbsp. cocoa powder in a small bowl. Whisk in 1/4 cup reserved milk mixture, then whisk in remaining milk mixture.
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5
When chocolate is melted, add cocoa mixture, espresso, sugar, and salt and cook, stirring often, until liquid begins to boil and thicken, about 4 minutes. Remove from heat and add amaro.
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6
Divide mocha among mugs. Top with whipped cream and dust with cocoa powder. Serve with caramelized brioche.
