Preheat oven to 325°F. Spray mini muffin tins with nonstick cooking spray.
Beat butter, shortening, and cream cheese with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, baking powder, and salt. Beat until combined, scraping the sides of the bowl occasionally. Beat in the egg and vanilla until combined. Slowly mix in the flour.
If dough is too sticky to handle, you can chill it for 30-60 minutes. Otherwise, continue below.
Shape dough into 36 balls (about 1 1/4 inches each). Lightly press balls onto the bottoms and up the sides of the muffin cups.
Make the filling: stir chocolate and butter in a small saucepan over low heat until melted. Remove from heat. Stir in egg, brown sugar, and vanilla and peppermint extracts. Spoon 1 slightly rounded teaspoon of filling into each dough-lined muffin cup.
Bake for 15-20 minutes until the crust is just firm and filling is puffed and set. Cool in muffin cups on a wire rack for 5 minutes. Carefully remove tarts from muffin cups; cool completely on a rack.
While the tarts are cooling, make the chocolate ganache. Place the chocolate in a medium sized bowl. In a small saucepan, heat the whipping cream over medium heat until it boils. Pour the cream over the chocolate and let sit 5 minutes. Stir until smooth.
Spoon a little ganache over each cooled tart. Sprinkle with crushed candy canes for garnish. Store in an airtight container for up to 3 days or freeze in a single layer in an airtight container or bag for up to 1 month.