Ours love green beans too! I buy fresh organic and steam them in the micro, then chop and add them to their meals. Haven't tried the canned or the frozen. I did try to puree some vegetables once for them and used cauliflower, brocolli, brussel sprouts and some others veggies, but they wouldn't eat it, so it was back to chopped vegetables. When they just want to play and I know they have had all their meals , we will give them a raw one to crunch on. They love them raw, but there is little nutritional benefit to them in that state, so they must be cooked.
Sounds like your little one is very spoiled and lucky indeed!