Preheat the oven to 350 degrees F.
Grease 3 (10-inch) cake pans with the 2 teaspoons of the butter. Line each with parchment paper and butter with 1/2 teaspoon butter. Set aside.
Place the cocoa in a bowl and slowly add the hot coffee, whisking until smooth. Set aside and cool.
In a large bowl, whisk together the sour cream and vanilla. Whisk in the cooled coffee mixture.
Sift the flour, baking soda, and baking powder together onto a sheet of waxed paper or into a bowl.
In a large bowl, with an electric mixer, cream the remaining pound butter and the sugar. Add the eggs 1 at a time, beating well after each addition. On low speed, add the flour mixture alternately with the coffee-sour cream mixture. Beat until glossy.
Divide the batter among the 3 prepared pans. Bake a cake tester comes out clean, 30 to 35 minutes. Let cool completely in the pans on a wire rack.
Remove the cakes from the pans and peel off the parchment paper. Using a long serrated knife, trim off the rounded top from each to make a flat surface. Place the first cake layer on a cake plate or stand. Spread about 1 1/2 cups of the chocolate icing across the top, out to the edge of the cake, and sprinkle with about 3/4 cup crushed butter toffee. Repeat with the second layer and another 1 1/2 cups icing and 3/4 cup crushed toffee. Place the third layer upside-down on top. Frost the top and sides of the cake with the remaining icing, and press the remaining crushed toffee onto the sides and top of the cake. Serve.
Combine the cream, butter, cocoa, and corn syrup in a large saucepan, and bring to a simmer over medium heat. Remove from the heat.
Put the chopped chocolate in a large bowl. Add the hot cream mixture and let sit for 2 minutes, then whisk until the chocolate is melted and smooth. Add the vanilla and almond extracts and whisk to blend. Cover and refrigerate until needed. (The icing will keep refrigerated for up to 3 days.)
Line a baking sheet with parchment or wax paper.
Combine the butter, granulated sugar, brown sugar, and cream in a medium heavy saucepan and cook over low heat, stirring occasionally, until the sugar dissolves. Continue to cook until the mixture reaches 300 degrees F, or the hard-crack stage (a drop of boiling syrup immersed in cold water crackles).
Remove from the heat, add the vanilla, and stir. Pour onto the prepared sheet and let cool completely.
Crack the toffee into large shards with a rolling pin. Place the pieces in a large deep pot and break into smaller pieces with the end of the rolling pin. Store in an airtight container until ready to use.