Heat 1 tablespoon olive oil in a large (4 to 6-quart) saucepan over medium heat. Add the onion and bell pepper along with a generous pinch of salt. Sweat for 5 minutes or until the onions are soft. Add the garlic and mushrooms and continue to cook for another 4 minutes.
Add the broth, peas, rice, coriander and cumin. Increase the heat to high and bring to a boil. Decrease heat to low, cover and cook at a simmer for 1 hour or until the rice and peas are tender.
Remove from the heat and gently pour the mixture into the bowl of a food processor and process until just combined.* Do not puree. Pour this mixture into a bowl and stir in the 3/4 cup of bread crumbs. Season, to taste, with salt and freshly ground pepper. Refrigerate for 30 minutes.
Shape the mixture into patties and dredge on each side in the remaining 1/4 cup of bread crumbs. Heat 1 tablespoon of olive oil in a medium saute pan over medium heat. Add 2 burgers at a time and saute until brown on each side, approximately 3 to 4 minutes per side. To grill, cook on high for 3 to 4 minutes per side as well. Serve immediately.
*When blending hot liquids: Remove liquid from the heat and allow to cool for at least 5 minutes. Transfer liquid to a blender or food processor and fill it no more than halfway. If using a blender, release one corner of the lid. This prevents the vacuum effect that creates heat explosions. Place a towel over the top of the machine, pulse a few times then process on high speed until smooth.