Lightly grease (or spray with Pam) one deep 9x13 rectangular cake pan. I would suggest a 4 in deep pan, as the cake rises when it is cooking, but a oven-safe disposable coffee cake pan from the grocery store would work fine too.
Melt butter. I do this by heating the the microwave on low power for 30 seconds.
Empty cake mix into a large bowl.
Stir melted butter, along with ONE egg, into the cake mix.
PRESS mixture into pan. Mixture will have the consistency of sticky dough. Using a spatula works for me, but pressing with clean fingers will do the trick as well.
In a large bowl, mix cream cheese, almond or vanilla extract, confectioners sugar and the remaining two eggs.
Beat for three minutes with an electric mixer set on medium high speed, or until smooth with NO lumps.
Pour evenly over top of the cake mixture in the pan. Use a spatula to spread.
Place a large cookie sheet on the rack below the cake. Sometimes when you use a cake pan with less depth, the cake bubbles and spills over. The cookie sheet will spare your oven! Bake at 350 for 30-45 minutes until golden brown on top. Cooking time is estimated, you will really have to watch it here! I always take the cake out when it turns a darkish golden brown. Note that there will be a paper thin sugar "crust" that will form while the cake is baking. It the top layer of sugar hardening, and this is what will turn golden brown. It adds great texture!
Allow cake to cool COMPLETELY. This is very important, as the cake will not cut easily until it is completely cool. You will notice that the cake has sunken and set. This is normal. Refrigeration is optional. I personally like it at room temperature.
Dust the top with confectioners’ sugar.
Cut cake into bars and serve with or without utensils, but make sure you have plenty of napkins, because this treat will have you licking your fingers! (Cake should be gooey underneath the sugar "crust", so don't over bake!).