Learn Farsi: من همه‌ی پارچه‌ها را به جز مخمل دوست دارم.

be joz means except or apart from. It is placed directly before the noun being excluded, which is maxmal (velvet) here. You treat be joz maxmal as a prepositional phrase, putting it right before the verb phrase dust dâram.

Why is the object marker râ placed after pârče-hâ and not after maxmal?

The direct object you are actually doing the liking to is hame-ye pârče-hâ (all the fabrics). Because it is a specific, definite direct object, it takes râ. The phrase be joz maxmal is an exception added to the sentence, not part of the direct object itself, so râ must come before it.

Why does the word hame (all) have a -ye attached to it?

That is the Ezâfe vowel linking the word hame (all) to the noun it modifies, pârče-hâ (fabrics). Because hame ends in a vowel sound, the Ezâfe is written and pronounced with a y sound, making it hame-ye to mean all of the.

Could I move the exception to the beginning of the sentence?

Yes! Just like in English where you can say Except for velvet, I like all the fabrics, you can move the be joz maxmal phrase to the beginning of the sentence for emphasis. Both word orders are perfectly natural in Farsi.