drowsy

Drowsy is formed from drowse plus the adjective-forming suffix -y, and traces back to Old English drūsian, meaning to droop, drowse, or become languid.

Oddly, drowsy is first recorded in 1520, a full fifty years before the verb drowse appears in 1570, reversing the order you'd expect for a word built from another.

It shares its root with drowse itself, both descending from the same sense of drooping or growing languid found in Old English drūsian.