Preheat oven to 375°F with oven racks in the top third and bottom third of oven. Beat butter and both sugars with an electric mixer on medium speed until smooth, about 1 minute. Add egg yolk and vanilla, and beat on low speed just until incorporated. Whisk together flour, salt, and baking powder in a small bowl, and gradually add to butter mixture, beating on low speed just until incorporated after each addition.

Drop dough by tablespoonfuls 1 inch apart onto parchment paper-lined baking sheets. Press your thumb or the end of a wooden spoon into each ball, forming an indentation.

Bake in preheated oven until cookies are set and beginning to brown, about 12 minutes, switching pans top rack to bottom rack halfway through baking. Cool on pans on wire racks 5 minutes; remove cookies to wire racks, and cool completely, about 30 minutes.

Combine chocolate chips and cream in a microwave-safe bowl, and microwave on MEDIUM (50% power) until melted and smooth, about 1 1/2 minutes, stirring every 30 seconds. Cool 5 minutes. Fill each indentation with about 1/2 teaspoon of the ganache. Sprinkle cookies evenly with crushed peppermints, and let stand 15 minutes before serving.