Caramelized sugars, changes to protein structure, the formation of unique compounds, etc. all create that meaty crust that we find so appealing. Food scientists are hard at work trying to uncover what exactly makes "browning compounds" so delicious (in no small part because they would like to figure out how to add these flavors to processed foods) but mysteries still about.
Some theories as to why we find these compounds pleasurable in the first place suggest that a nicely browned crust indicates cooked meat. The human gut was not initially a carnivorous one. Our shared ancestor with the chimpanzee likely has a more chimp like chimp-like diet of primarily fruit supplemented by a smaller portion of hunted game. When we moved to the savannah and began to rely on animal flesh for a greater portion of our nutrition, those who enjoyed cooked meat were able to consume/assimilate calories more efficiently. A survival advantage of only 1% is enough to increase a gene's frequency to 99% within a population after only a few thousand generations and we spend way more time than that as plain dwelling Pleistocene hunters.
Of course, this is just conjecture, but the fact that we do enjoy (and are "rewarded" by) a nice crusty piece of meat with a moist, juicy center indicates that there is some sort of survival advantage signalling at work.