With drops of sugar and honey, milk producer prepares shake (7)
I believe the answer is:
shudder
'shake' is the definition.
(I've seen this before)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for shudder that I've seen before include "Shiver in fear or revulsion" , "Shake, quaver" , "Vibration" , "Shake convulsively" , "Convulse" .)