刀削面: who says xuē and who says xiāo?
I believe xiāo is the correct pronunciation, although xuē can also be correct in certain regions; it depends on how you pronounce 削 in its &quot;shave&quot; meaning.
削 has two pronunciations depending on usage, although both can mean &quot;shave&quot;:

削 xiāo 　ㄒㄧㄠˉ
　1. 用刀斜着去掉物体的表层。～苹果皮。～铅笔。
　2. 打乒乓球时用球拍平而略斜地击球：～球。
削 xuē 　ㄒㄩㄝˉ
　1. 义同削（xiāo），用于一些复合词：～铁如泥。～足适履。
　2. 减少；减弱：～减。～弱。
　3. 除去：～职为民 。
　4. 搜刮；掠取：剥～。

xiāo is the pronunciation used for the &quot;shave&quot; verb, but as you can see, xuē also means &quot;shave&quot; in certain phrases, like 削铁如泥. Apart from that, xuē is usually used in the &quot;pare&quot; or &quot;reduce&quot; meaning, as in words like 削减.
Since 刀削面 is supposed to mean &quot;knife-shaved noodles&quot;, the pronunciation should be based on the one for &quot;shave&quot;. This is usually xiāo, but in some dialects it is xuē.