Note: You can substitute store bought French vanilla ice cream, if you absolutely have to :-)
In a large heavy pot, combine milk and cream and place over medium heat, stirring every few minutes. Just before it begins to boil, remove from heat.
Combine the egg yolks and sugar in a mixing bowl. Whisk until well blended and creamy looking.
To temper the eggs, (keep them from becoming scrambled chunks) use a large ladle to incorporate the hot milk mixture into the sugar/eggs. Whisk one ladle full in at a time until 3/4 of the milk is incorporated. Add the egg/milk mixture back to the pot and stir well.
Turn the heat back on to medium. Stir constantly and cook until the mixture reaches 180 degrees F. Do not allow it to come to a boil.
Strain the mixture through a fine wire mesh sieve. Add the mascarpone cheese and vanilla. Stir until all the lumps of cheese have dissolved.
Take a piece of plastic wrap and lay it directly on top of the mixture to keep a skin from forming. Place in fridge until completely cold. (overnight is best)
Place the mixture in ice cream maker canister and process according to the manufacturer's directions.
While the ice cream is processing, make the sauce. Place the chocolate, 1/4 cup coffee and vanilla extract in a small sauce pan over low heat. Once the chocolate begins to melt, stir constantly until all is melted. Set aside.
In an 9 x 12 x 2 baking pan, pour enough ice cream in to cover the bottom. (about 1/2 inch thick)
Mix the 1/2 cup coffee and Kahlua in a small bowl. Dip the lady fingers in to coat. (do not soak)
Place the cookies on top of the ice cream, arranging them in an evenly spaced layer.
Pour the rest of the ice cream on top of the cookies. Spread with a spatula to smooth and cover with plastic wrap. Place in freezer to harden the ice cream for about 1 1/2 hours or until firm enough to slice.
Remove from freezer. Run a large knife under hot water and slice into desired serving sizes. Coat the serving dishes with a light dusting of cocoa powder. Place the slices on the dishes and drizzle the chocolate sauce on top.