I annoy constantly with bit of obscene sauce (5)
I believe the answer is:
pesto
'sauce' is the definition.
(I've seen this before)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for pesto that I've seen before include "sauce involving Basil" , "Pasta sauce mainly of basil and cheese" , "Sauce of basil, pine nuts, etc" , "Pasta sauce based on basil" , "Basic sauce" .)