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If one were to want to add spices, herbs or other interesting bits to their cheese as is done with the pepper jack or caraway cheddar cheeses I see in the stores, at what point in the process would I add this ingredient?

It is written u do it after u create the curds, add the flvorings and then mix and put in the molds.
I did havarti and but the seeds in at the beginning so they would soak (the idea was), dont know how it will end up. Would go with what they say.

a little late, but, it is also written that you put it in earlier: poach the herb or spice in a little water, strain the water into your milk. retain the additive and add to the curds when milling.
i've made various flavoured cheddar-types successfully following this process

Just for diversity I've seen some goats cheese recipes where flavourings such as celery seeds or Ash are added to the outside of the cheese after it comes out of the mould. I think most of these were log shaped cheeses.

FB

experiment sparingly with ash , and make sure it's sieved very finely
celery seeds (and minced garlic) make a tasty internal and external soft cheese flavouring

Thanks for the replies.

Ash, huh? What is it's function? A flavoring or a protective coating?

if using vegetable (ie edible food grade) then a bit of both
if wood ash, then only as an aesthetic, mildly protective (against some moulds)
i would say