Preheat the oven to 350o Butter and flour 2 (9-inch) round cake pans.
Whisk together the flour, cocoa powder, salt, baking soda, and espresso powder in a large bowl and set aside.
Add the sugar and eggs to a blender or food processor and process until combined; add the mashed potatoes, milk, oil, and vanilla extract and pulse until smooth, scraping down the sides as necessary. With the motor running, slowly drizzle in the unsweetened chocolate.
Add the wet ingredients to the dry and beat until combined.
Pour the batter into the 2 prepared pans and bake until a wooden pick inserted inside comes out clean, about 20 to 25 minutes. Cool completely on wire racks.
For the ganache, melt together 12 ounces of the semisweet chocolate with the half and half and butter in a double boiler or microwave. Gently stir until combined, and then cool to room temperature. Once at room temperature, whip the chocolate mixture with a handheld electric mixer until light and fluffy, about 1 minute.
To assemble the cake, place 1 of the cake rounds onto a cake platter. Spread about 1/3 of the whipped chocolate ganache on top. Place the other cake round on top and spread the remaining whipped chocolate ganache on the top and sides.
Melt the remaining 4 ounces of semisweet chocolate and let it cool until it’s no longer hot, but is still pourable. Spread the melted chocolate on top of the cake and let it drip down the sides. Let the chocolate set before slicing and serving.
Store any leftover cake covered in the fridge for up to 3 days.