Pre-eminently is the adverb. It means in a way that stands clearly above the rest — most of all, above all, as the thing that most defines someone or something. “She is pre-eminently a teacher” means teaching is what she is first and most, even if she does other work. You can also use it to say something is true to a very high degree (“pre-eminently suited to the job”). It is a formal, bookish word; in ordinary talk people say above all, especially, or more than anything. Same hyphen habits as the adjective: British writing often keeps it; American writing often drops it.