刀削面: who says xuē and who says xiāo? I’ve only ever known 刀削面 as dāoxuēmiàn, maybe that says something about the company I keep.
I’ve noticed recently a lot of people, though, actually say dāoxiāomiàn.
ABC dictionary lists both pronunciations, with slightly different meanings:

dāoxiāomiàn
N.
shaved noodles
M: wǎn / 碗
See also dāoxuēmiàn

and

dāoxuēmiàn
N.
hand-cut noodles
M: wǎn / 碗
See also dāoxiāomiàn

Also, quite bizarrely 汉语大词典 has

dāoxuēmiàn
面食之一。先将面加水和成硬面块, 然后用刀削成片状, 煮熟食用。此法盛行于 山西 一带。

While 现代汉语大词典 has almost exactly the same definition (minus the spaces around Shanxi) under a different pronunciation:

dāoxiāomiàn
面食之一。先将面加水和成硬面块, 然后用刀削成片状, 煮熟食用。此法盛行于山西一带。

So, ABC says that they are two different things - while the two big dictionaries say they’re the same thing and differ in pronunciation.
Who says what? And are they the same thing even? Or are they separate entities?
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.