Time to "tech" it up... Produce the glass form with a 3D cookie dough printer. Either the dough at the bottom can be thicker or the composition of the dough can be more dense. Through trial and error (and much gnoshing), I will arrive with a cup that is precisely calibrated to absorb enough milk for the desired amount of moistness for a 5 minute sip-n-bite session.
Edit. Need to build in a non-cookie reservoir at the bottom, so one can get that last sip of cookie-infused milk to wash it all down.