Of the cuisines of the South Caucasus countries, Georgian provides the most options for vegetarians. Armenia is awash with the tastiest fresh fruit in the summer and autumn months and greens and vegetables figure large in the diet, but they are usually served as accompaniments to a main dish of meat kebabs and in most traditional restaurants you'll struggle to get more than a plate of cheese, bread and tomato and cucumber salad. You can of course order a veggie kebab, which usually involves skewering aubergine, pepper and tomato, and maybe a potato or two and sticking it on the grill among the lamb....
I haven't visited Azerbaijan, but my daughter reports it is extremely difficult outside the main towns to find veg food. Most village restaurants don't have menus as they only serve kebabs: either chicken or lamb. She survived on bread and tea most of the time, with the occasional treat of a tomato and cucumber salad.
If given the choice then, Georgian cuisine is the one for veggies. If you're lacto-veg, then you have the option of chowing down on the ubiquitous khatchapuri, a traditional flat bread stuffed with cheese, but vegans will also find plenty of variety. Stuffing vegetables with walnut paste is a Georgian trick, as is flavouring salads and said stuffed veggies with pomegranate grains or juice. Beans figure large, too. You'll often find green beans or red beans, cooked with garlic and walnuts and lots of herbs. Herbs are a very distinctive feature of Georgian cooking, in contrast to the dishes of Armenia and Azerbaijan which are rather plain. Georgian cooks often use a mixture called Khmeli Suneli, which has just about everything in it. It's hard to find outside ex-Soviet countries, but you can achieve a similar result by throwing in a mixture of most of the components. Basil, coriander, savory, mint, dill, garlic, black and red pepper and cinnamon are the main ingredients.
This is a traditional Georgian soup we're were substituting the usual chicken bullion for veggie bullion and making our own version of khmeli suneli. The quantities are enough for four or five people.
Half a cup of rice
Half a cup of pomegranate juice
1 cup of shelled walnuts
1 onion
1 or 2 cloves of garlic
A teaspoon of tomato puree
1 veg stock cube
A pinch or two each of ground black pepper, coriander, cinnamon and red chilli
A mix of any or all of the following fresh or dried herbs: mint, dill, basil, parsley, savoury, celery leaves, coriander leaves
Salt
Olive oil
2 litres of hot water
Chop the onion and fry gently in olive oil until transparent. Add the rice and fry for a few more minutes, then add the water. Bring to the boil and simmer for five minutes before adding the tomato paste, pomegranate juice, stock cube, ground spices and chopped or ground walnuts. Simmer for another ten minutes or so, adding salt to taste. When the rice is tender, remove the pan from the heat and stir in chopped fresh herbs (or a few pinches of dried) and chopped garlic.