If you want to actually get full and satiated with a largely vegetarian diet, you will eventually resort to carbs

And this is for a culture that really knows how to make smashingly good vegetarian dishes

I love my vegetables, but a vegetable-heavy diet is clearly not something that everyone can or should do. The people I know who retain their health with vegetarian/vegan diets are usually really well-versed in nutrition

Carbs and butter.

If you look at a lot of the indian vegetarian dishes you'll find things like potatoes fried in butter being a staple.

Chickpeas and yogurt do make a showing, but a lot of indian dishes are devoid of vegetarian protein sources. You need a lot more beans/nuts if you want to eat healthy as a vegetarian.