Tropicals & Tender Perennials: Monika, more help needed, lol, 1 by Calalily

Calalily wrote:
Are these hopeless? I have a lot of brugs that look like these, they didn't freeze all the way to the ground, but did die back below the Y. Should I chop this all the way back and start over? Help, I'm afraid I'll make a bigger mess.
The leaves are tattered from a wind storm, so ignore how bad they look. They are growing new leaves but I didn't remove the old ones so no one could see the ugly "sticks" that would be left.