Preheat oven to 350°. Grease and flour two 9" round baking pans.
Melt the chocolate in a microwave safe bowl in 30 second intervals. Stir the chocolate between intervals until it is completely smooth. Make sure not to over heat the chocolate or it will seize.
Add the flour, cocoa powder, baking powder, baking soda and salt in medium bowl and stir to combine.
In another bowl, beat together the sugar, eggs, milk, vegetable oil, vanilla and melted chocolate.
Slowly add the dry ingredients into the wet ingredients. Mix well scraping down the sides.
Add the hot espresso and mix slowly until it is fully incorporated. The batter will be thin.
Divide the batter between the two pans and bake for 30-35 minutes or until a tooth pick inserted in the center of the cake comes out clean.
Cool the cakes in the pan for about 10 minutes and then transfer them to a wire rack to finish cooling before frosting.
Beat the mascarpone in a medium bowl until the cheese and creamy, about 1 minute. Add the heavy cream, confectioners sugar and vanilla. Beat for about 2 -3 minutes just until peaks form and they hold their shape when the beaters are lifted out of the frosting. Check the consistency of the frosting often while beating it so that you do not over mix the cream. If you over beat the cream it will curdle.
Frost the cake as desired. The cake is best when refrigerated for about an hour before serving.
The cake can be covered and stored in the refrigerator for 4-5 days.