Breads on Oak - having a child with Dairy allergy- this place is our go to- be advised its ALL VEGAN. ( they recently added Impossible burger to menu- but thats as close as you will get to anything "meat" )
And their pastries are really really good. And i can vouch for the bread- multi grain ( whole or half loaves ) and baguettes
I just thought of Mona's Cafe for Mediterranean -
Mona's Cafe
3901 Banks St, New Orleans, LA 70119