Part of Speech, Broke-up vs Broke up

In the following sentence, broke-up is an adjective, correct?

Brad and Jennifer broke-up with their friends

Now if we remove the hyphen, i.e:

Brad and Jennifer broke up with their friends

what is the parts of speech for 'broke' and 'up' ?

Brad and Jennifer broke up with their friends.

No, it's not an adjective. "Broke" is a verb and "up" is a preposition. Some people call this a phrasal verb, but that term is misleading since it is only "broke" that is a verb.

In your example, “broke up (with their friends)” is a constituent, but it’s not a constituent at word level. "Broke up" is a verb phrase in which it’s just "broke" that is a verb: this is the word that takes verbal inflections.

So we have [1] but not [2]:

[1] B & J broke up.

[2] * B & J break upped.