Well if I was gonna make it, I would brown the burger first or its gonna be greasy.
Going with simple, I'd salt and pepper it. (if I get one fancy, it would be some garlic powder or maybe oregano.)
If using real rice, its about a 2 to 1 ratio of liquid to water, maybe a little more liquid. So just using tomatoes as the liquid source, i would want to use 3 or 4 maybe. Chop them up and be sure to save the juice to add.
I'd probably heat it for a while, see how much liquid was developed, then add enough stock or water to just cover. Then simmer for however long the rice said.
Wouldnt peek, just like with rice.
As for fresh and juicy tomatoes.. got any gardeners living nearby who might part with a few?
Let us know how this turns out. It sounds familiar but darn if I can remember from where!