With some pictures from the monastery next door.

A site on the web has "Church of the Cross (Turkish, Haçlı Kilise) in Red Valley is a cave church featuring a splendid stone cross on the ceiling and a fully painted apse. With an amazing apse scene, a monumental ceiling relief, and a stunning view of Red Valley, Church of the Cross is one of Cappadocia’s best churches to visit." Maybe "Red Valley" should be "Rose Valley". As several other churchesa have crosses the Turkish name seems preferable.

Note I have grouped many churches in Cappadocia in one gallery.