In the bowl of stand mixer, whip heavy cream with 1/2 Tbsp sugar and peppermint extract. Whip until stiff peaks form. Fold in candy canes. Keep cool until ready to serve.
Preheat oven to 450 degrees. Butter and lightly flour 4 ramekins.
In a double boiler, melt butter and chocolate together until smooth.
In a large bowl, beat together eggs, egg yolks and sugar until light yellow and thick, approximately 2 minutes. Beat in flour until well-combined. Stir in chocolate until combined.
Divide batter between the four ramekins. Bake for 8 minutes.