Put the chopped semisweet and milk chocolate in a medium bowl. Bring the heavy cream and butter to a simmer in a small saucepan. Pour the cream mixture over the chocolate, completely covering it, and let sit for 5 minutes. Stir with a spatula until the chocolate is completely melted, smooth and glossy. (If the chocolate doesn't melt completely, microwave the mixture on high in 15-second increments, stirring in between, until fully melted.) Fold in the bourbon and peppermint extract until they are incorporated. The mixture will look separated at first, but keep stirring until it is uniform.
Set the bowl over a larger bowl of ice water, and let the mixture chill for 3 minutes, stirring occasionally, until it has thickened a bit and become homogeneous. Pour the mixture into a shallow 2-quart baking dish or 9-inch pie plate. Cover with plastic wrap, and refrigerate until set, about 3 hours.
Meanwhile, process the sugar and mint in a food processor for 1 minute until the mint is finely chopped and dispersed, scraping down the bowl with a spatula halfway through. (The mint sugar can be refrigerated in an airtight container for 2 to 3 days.)
Scoop tablespoon-sized balls of the chocolate mixture, and roll them between gloved hands to shape them, working quickly, as the balls melt fast. Put them on a plate or rimmed baking sheet, and refrigerate for 10 minutes. Put the mint sugar in a shallow dish, and drop the balls in a few at a time, shaking the dish to coat them on all sides; transfer the truffles to a platter, shaking off the excess, and refrigerate until you are ready to serve them. (Once the truffles have been coated, they must be served that day. Uncoated, they can be stored overnight in the refrigerated in an airtight container or covered with plastic wrap, then coated the day they're served.)
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