Melt the chocolate chips in a microwave-safe bowl in 30-second bursts, stirring between each, until smooth, about 90 seconds. Let cool for 5 minutes.
In a large bowl, beat the cream cheese and powdered sugar together until smooth and fluffy, about 2 minutes.
Beat in the melted chocolate until fully combined.
In a separate bowl, whip the heavy cream and peppermint extract to stiff peaks, about 3 minutes.
Fold the whipped cream into the chocolate mixture in two additions, being careful not to deflate it.
Spread the filling into the crust and smooth the top.
Freeze uncovered for 1 hour, then cover and freeze at least 3 more hours, until firm.
Top with crushed peppermint candies just before slicing.