My original plan was to visit Café N, that has been recommended to me, but it was too crowded for me, so I opted for Kimia - not a disappointment.
I had some (quite filling!) crackers with homemade tahini, tomatoes and greens, and it was delicious.
Friendly service, wi-fi and free water (not a given in Denmark). Will return for brunch when I can.
Updated from previous review on Monday June 16, 2014
Updated from 4 to 5: I had the chance to visit for brunch and I was not disappointed. Brunch is vegetarian by default, and a vegan option is not on the menu, which I think they should definitely update, because what she combined for me was absolutely delishes, and I will definitely be back again. I wish they would make it all vegan though.
Also, I'd like to add how friendly the service was - very big plus!
Cons: Few vegan options