I was wondering how one should adapt one's diet to optimize bone reconstruction efficiency.
Popular knowledge tends to highlight the need for calcium, but I'd like to know if there are any scientific recommendations for this case
This answer would be most likely the same for a non-veg*n question, since there is nothing specific that you should look out for as a result of your diet.
The bones are made mostly out of rigid form of collagen, which is a protein and composes the organic part of the bone and calcium phosphate and other salts, which create the hard outer layer.  Based on all this you want focus on three main things when recovering from a broken bone:
For the first point, you don't really need to overdo it and normal/a bit higher levels of protein intake than in your regular diet should be alright. You can easily handle this with the usual vegetarian combo of dairy, eggs and nuts with some vegetable protein sprinkled on top. Just make sure the sources of protein are varied as this increases the likelihood of all of the essential amino acids being present in your food.
The second point would be mainly about getting sufficient, if not increased, amounts of Vitamin D, which, through its increase in calcium absorption, helps to maintain healthy bones. Vitamin D can be synthesized by your body from skin exposure to sunlight, but, particularly in winter and/or not very sunny places, this is not enough. Food sources vary depending on the type of Vitamin D. D3, which is in general the preferable one, can be found in eggs and that's basically it for veg*n sources. However, D2 is to be found in some mushrooms and is used to fortify a lot of vegan (and perhaps vegetarian) food as well. However, be wary of Vitamin D caused hypercalcimia as this can have some serious adverse effects on your body (we are talking about huge doses here though).
As for the last point, this can be influenced by Vitamin C. Vitamin C is helpful in collagen synthesis, which, as mentioned before, makes most of the organic part of your bones. At this point, I would also add a "not only" to that statement, as collagen makes up a lot of things in your body and the effects of its improper synthesis due to the Vitamin C deficiency once caused sailors rather big problems. You may have heard of it being called scurvy. So you want the exact opposite of that and that means a lot of Vitamin C. Almost any fruit and vegetable there is will add some Vitamin C into your system, but fruits are generally better in this regard, with the top picks being citrus and berry fruits along with tropical ones like mango, watermelon and papaya. And the best part is that, unlike with Vitamin D, there is no risk of hypervitaminosis from Vitamin C; any excess Vitamin C you ingest will be excreted in urine eventually (but very high doses can cause temporary diarrhea).
Honourable mentions are also Iron and Potassium. Iron helps keep your red blood cells in good shape and delivering the much needed oxygen to the injured tissues so that it heals faster. Potassium helps keep the calcium you digested in your body for longer by stopping you peeing out so much of it.
I think I should also mention what you should not do as there are things that can have a negative effect on your bones.
The biggest no-no is probably excessive salt intake, since sodium actually weakens your bones by decalcifying them. Alcohol has many adverse effects on your bones as well and so it would be a good idea to abstain from it while you recover. There as also been some talking about adverse effects of caffeine on your bone health, but the evidence is not very convincing at the moment and so you should not worry about this much.