Since 1871, six generations of the Güllüoğulu family have been churning out pistachio-encrusted and syrup-soaked baklava to the masses. There's also kadayıf (dough soaked in syrup and topped with a layer of clotted cream) and plenty of other sweet pastry pistachio-laden treats that will give your dentist nightmares.
To find it, scoot into the main alleyway of the Elmacı Pazarı. It's about 5m down on the left.