Believe it or not, there is a vegetarian movement in Buenos Aires, and the Restaurante Abuelapan in the San Telmo district is one of the best. I have eaten there several times and ordered vegetarian steak milanese, and several Italian dishes that were indistinguishable from real meat dishes. Better and cheaper, said to be lower in calories and cholesterol, they are just as filling as dishes made with beef.
Argentina and Uruguay, of course, have the best steaks you will find anywhere.
There is a sort of small pumpkinlike squash called a zapallo that I have never seen in the US or Mexico that is frequently used in these dishes. It is amazing what some skill in the kitchen can do to vegetables to make them resemble meat.
http://www.abuelapan.com/