Preheat the oven to 350 degrees F. Lightly butter 2 ovenproof 6-ounce tea or coffee cups. Tear a loosely packed 1/2 cup of the croissant pieces into slightly smaller pieces, and toss them with the melted butter in a small bowl; set aside.
Whisk the egg with 2 tablespoons of the sugar in a medium bowl until the sugar is dissolved. Whisk in the half-and-half and vanilla. Stir in the remaining 1-inch croissant pieces and the caramels, and let the mixture sit, folding occasionally, for about 15 minutes. Don't worry if the mixture seems too wet; the excess moisture will be absorbed as the pudding bakes.
Divide the soaked bread mixture between the prepared cups. Top each with half the buttered croissant pieces, and sprinkle with 1/4 teaspoon of the remaining sugar. Bake until the bread pudding puffs above the rim of the cups and is set, about 30 minutes. Let cool a few minutes (the pudding will sink), and serve warm.
Copyright 2015 Television Food Network, G.P. All rights reserved.