Bring a pot of water to a boil and cook the broccoli for 2 minutes. Drain and lay the broccoli on a plate lined with paper towels.
In a large pan, melt the butter. Add the mushrooms, garlic, oregano and cumin. Stir until the mushrooms are soft. Let cool.
Finely chop the broccoli and add it to a large bowl.
Chop the mushrooms and add to the bowl with the corn and diced onion.
Add the beaten egg and season with the salt and pepper. Mix to combine.
Add the flour followed by the cooked brown rice and fold through.
Using a spoon, fill a 1/2 cup measuring cup with some of the mixture, packing it tightly.
Turn the cup over and dump the burger out onto a baking tray lined with parchment paper.
Repeat this process using extra flour if things get sticky. You may need to wash your hands a few times also.
Once all of the burgers are on the tray, sprinkle the tops with a little more flour and gently press down with the palm of your hand making the burger thinner (it'll cook faster this way.
Heat the oil in a pan and over a medium heat, saute the burgers for about 5 minutes each side checking that they don't get too brown.
Serve the burgers on brioche buns with some lettuce leaves and spread if desired.