As far as I remember serving meat for guests has been an essential sign of respect. Iranians are obsessed with lamb, beef and chicken as these are the main ingredients of lots of stews and kebabs.
There are lots of vegetarian Persian dishes all over the country but I personally believe that the love for meat has in a way made us a little negligent to our vegetarian dishes.
I was born and raised in Iran and I have heard guests gossipping about the hosts' food if the quantity of the meat chunks did not live up to their expectations. They simply considered it rude and lack of respect for guests. However, I believe that Iranian vegetarian dishes are a feast on their own.
People of the north of Iran have a vast variety of vegetarian dishes. Eggplant, garlic, tomatoes, walnuts and eggs are mainly the quintessential ingredients of their dishes. In Mashad and Isfahan Kal-Joosh is one of the simplest and most delicious vegetarian dishes. This dish can be made by bringing to boil whey or yoghurt and adding fried onion and garlic in turmeric and mint oil.
Yatimche or Orphaned food is also another very simple and loved vegetarian dish in Iran. You can simply layer in a pot circles of onion, paprikas, potatoes, zucchini, tomatoes and eggplants and make a red sauce with tomato paste loosened in water mixed with minced garlic, salt and pepper and poured over the vegetables, cooked on a low heat for 45 minutes and it turns to the most delicious and least intricate vegetarian dish.
Kuku sabzi (green kuku/frittata) is also one of the healthiest and simplest vegetarian dishes in Iran that is often served on New Year's Eve to celebrate the beginning of Spring with the greenness of Kuku.
The love for meat aside, Iranians are becoming more and more willing to cook their vegeterian dishes these days. Is it for the huge interest in vegetarianism or the high prices of meat, I really don't know but I know for sure that Persian vegetarian dishes are extremely delicious and must not be neglected at all.