The irritability of the sandwich man? (10)

I believe the answer is:
crustiness
'the irritability of' is the definition.
The definition suggests a singular noun which matches the answer.
'sandwich man?' is the wordplay.
I cannot quite see how this works, but
'man?' could be 'rustin' and 'rustin' is present in the answer.
The remaining letters 'cess' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
'the' is the link.
Can you help me to learn more?
I've seen this clue in the Evening Standard.
Want a hint initially instead of a full solution?
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