I met her
in a shop
downtown.

She was buying a hat
with a feather.

"Brown" -
she said.
"Or red."

That's all she said:
'BROWN'

When the rain falls
on our head,
think
of the time
when we met
in a shop
downtown...

"Feather
Brown" -
she said.
"Or red."

That's all she said:
BROWN

[...]

The style is very Dickinson-esque, but she used dashes instead of periods.

I would suggest we keep this discussion limited to literary works. Since this is a song, you may want to post it here. I won't give away the answer, but I will say the only thing it has in common with Dickinson is, well, nothing.