If I was you I would try adding some coconut oil, coconut milk and avocado to his diet on a regular basis. We're not vegetarian, but I recently was going through something similar - dd (20 months) wanted to eat constantly, had major mood ups and downs, and really mostly was just craving breads, crackers, etc. We changed our diet to a very consistent high fat one for a couple weeks (every meal was planned out - the whole story of why is a long one, but in a nutshell I realized me and dd both have a systemic candida problem), and things totally changed. Her poops contained much less undigested food, her moods were very even, and she ate 3 meals and 2 snacks a day. She was a much happier child. Unfortunately, we fell off track, but that's another story.
Now, I believe that everyone needs saturated fats, but even those who advocate lowfat diets would concede, I'm sure, that children, especially babies and toddlers, need lots of it for their growing brains, which is why I suggest the above fats. I also believe cholesterol is important, although your ds would be getting that from your breastmilk, so that's a good thing. You could try putting raw egg yolks in smoothies for him as well.
Another thought I just had - are you newly pregnant? When I got pregnant, dd (at about 15-16 months) had been about 98% breastfed, and suddenly she started eating tons of solids - just a thought.