Step 1Heat the oven to 350 degrees. Melt the chocolate using a double-boiler, or in a microwave, stirring every few seconds. Set aside to cool slightly.
Step 2In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a hand mixer, cream the butter. Gradually add three-fourths cup sugar, beating until the mixture is light and fluffy, 3 to 5 minutes. Beat in the melted chocolate. Beat in the egg until combined, then the corn syrup. Beat in the peppermint and vanilla extracts.
Step 3 In a separate bowl, whisk together the flour, baking soda and salt. Stir the flour mixture in with the chocolate mixture, then stir in the crushed peppermint candy.
Step 4Shape the dough into 1-inch balls, and roll the balls in the remaining one-half cup sugar. Place the balls on a parchment-lined baking sheet, spacing the cookies about 2 inches apart. Bake the cookies until the edges are set, 12 to 15 minutes.
Step 5 Cool the cookies on the baking sheet for a few minutes before transferring to a wire rack to cool completely.