Bake chocolate cakes, set aside to cool.
To Make Filling:
Place cream in a medium saucepan and heat until just before it boils, about 5 minutes. Place chopped chocolate in a food processor and pour in hot cream, processing until the chocolate is completely melted. Turn off the processor, then add the butter and vanilla. Pulse until incorporated. Transfer chocolate to bowl of electric mixer. Chill until slightly stiff; about an hour in the refrigerator or two hours on the counter. Whip the filling with an electric mixer until lightened, 2 to 3 minutes.
Place 1 1/2 cups of filling to the side to frost the top of the cake. Add the chopped toffee to the the remaining filling and mix until combined to use for the filling and sides of the cake.
To Make Toffee:
1 ½ cups sugar
1 ½ cups (3 sticks) unsalted butter
Vegetable oil for pan
Oil a cookie sheet and set aside. Combine sugar, butter, and 4 ½ tablespoons water in a medium saucepan over medium-high heat. Cook while stirring constantly until the mixture reaches 300 degrees, about 16 minutes. A candy thermometer is highly recommended!
Once the mixture reaches 300 degrees, immediately pour onto cookie sheet, spreading evenly. Let stand until completely cool and hardened.
Tap the cooled toffee with a spoon to crack into pieces. Save about a third of the toffee pieces to decorate the sides of the cake with.
Assembly:
Top one of the chocolate cake layers with 1 cup of the toffee ganache filling. Place second cake layer on top. Cover the sides of the cake with the remaining filling. Spread the plain filling on top of the cake.
Place the cracked toffee around the sides of the cake until completely covered. Decorate the top as desired.