Crossword Genius

Rich confection set beside woman crossing river (5,4)

Ross

I believe the answer is:

lardy cake

I'm a little stuck... Click here to teach me more about this clue!

'rich confection' is the definition.
(I've seen this before)

'set beside woman crossing river' is the wordplay.
I cannot quite understand how this works, but
'set' could be 'cake' (I've seen this before) and 'cake' is present in the answer.
'river' could be 'r' (abbreviation for river) and 'r' is found within the answer.
'woman' could be 'lady' (lady is a kind of woman) and 'lady' is found within the leftover letters.
This accounts for all the letters.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for lardy cake that I've seen before include "Rich confection" , "Food" , "Rich bready cake" .)

I've seen this clue in The Times.
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