Trial and Error, and then some success:
A few years ago, when our son Jarrod was visiting, he cooked up some vegetarian cheese burgers for us one night.  Those were the best Vegetarian burgers I have ever tasted!  I remember him using a few simple ingredients: leftover cooked brown rice, cooked lentils, 1 grated carrot, sauted onions and garlic, seasonings.  I have been trying to replicate those burgers ever since…the flavor was there, but the texture was not.
This first batch I made did not include the bread crumbs.  I cooked them up and the texture was still not quite there, so once cooled, I mashed the burgers up, cheese and all, and added in the bread crumbs….shaped into patties and recooked.
This time it worked.  These are delicious in a bun with all the toppings, or on their own with a salad, and they even tasted better cold on a sandwich bun the next day.  A good way to use up extra cooked rice, and healthy too!
¾ cup brown lentils, rinsed
1 ¼ cups water
¾ cup leftover cooked brown rice
2/3 cup gluten free bread crumbs
½ cup sweet rice flour
2/3 cup grated aged cheddar cheese (Parmesan cheese would be good too)
few drizzles of olive oil
½ of a large onion, diced
4 minced garlic cloves
1 grated carrot
4 finely minced crimini mushrooms
salt and pepper to taste
2 tsp. Cumin
1 tsp. Garham Masala
In a mediums sized sauce pan, bring the water and lentils to a boil, cover with a lid and turn down to a simmer, cooking until the lentils are tender, about 40 minutes or so.
Meanwhile, heat up a frying pan on low to medium heat, with a drizzle of Olive Oil, add in the mushrooms to brown.  When browned, add in the onions and minced garlic, diced carrots, stirring to combine.  Add salt and pepper, and seasonings, stirring occasionally.  Cook about five minutes, then add in a light splash or two of water, and continue to cook on low heat.
Once the lentils are cooked, transfer to a food processor, with the rice and vegetables.  Blend to a puree, scraping down the sides 2 or 3 times, the mixture is quite thick.  Then return the mixture to a bowl, taste for extra seasonings, then add in the fine white rice flour, mixing well to combine. (I questioned adding in rice flour with the already bread crumbs...but it worked)
Shape into patties, and cook in a frying pan with a drizzle of olive oil, on medium heat. ( I forgot to time the burgers) but once nicely browned, flip over and add on a slice of cheese.  Continue to brown and cheese is nicely melted.  Since this was my 2nd go around, I did not add any more cheese....they were yummy!