Literal translation
The fine first (one)
Meaning
the very first
Explanation
Names the very first, the word bèu here not meaning handsome but carrying an intensifying force, as in siés un bèl ome, which doesn't mean you're a handsome man but you're someone who overdoes it. The phrase is so common that people almost always say lou bèu proumié rather than just lou proumié, with a feminine la bello proumiero. The same pattern gives lou bèu darrié for the very last.