I see ...
So i can only hope that quarterstaff will get Versatile attribute so my monk can keep one hand empty. Corect?
//Edit:
Incorect.

Acording to this discusion:
https://www.reddit.com/r/DnD/comments/6d1h63/if_a_monk_uses_a_quarterstaff_with_2_hands_for/Monk uses both hands only when attacking with quarterstaff ... so he can easily use all benefits ... 1d8 dmg, bonus unarmed strike (or flurry of blows), and deflect missile.
Thats a relief.