By far the most interesting religious building in Monastery Valley, this small monastery, centred around a small courtyard and semi-built into rock cones, was rebuilt in the 1870s. The gate is padlocked so before you come out here, ask for the key at the tourist office, above the teahouse next door to the Ayios Kostantinos-Eleni Kilise.
Be aware that you're likely to just be told it's closed if you're a solo traveller. Staff at the tourist office are much more willing to open it up if you're part of a group.