Came across house by the end of cobbled way (6)
I believe the answer is:
method
'way' is the definition.
(method is a kind of way)
'came across house by the end of cobbled' is the wordplay.
'came across' becomes 'met' ('meet' can be a synonym of 'come across').
'house' becomes 'ho' (abbreviation for house).
'by' says to put letters next to each other.
'the end of' suggests the final letters.
The final letter of 'cobbled' is 'd'.
'met'+'ho'+'d'='METHOD'
(Other definitions for method that I've seen before include "particular procedure" , "Type of acting" , "Systematic procedure" , "Orderliness (of thought or behaviour)" , "Procedure or system" .)