Heat 1 tablespoon olive oil in a large saucepan over medium heat. Add the onion and bell pepper along with a generous pinch of salt. Sweat until the onions are soft, about 5 minutes. Add the garlic and mushrooms and continue to cook for another 4 minutes.
Add the broth, peas, rice, coriander, and cumin. Increase heat to high and bring to a boil. Decrease heat to low, cover, and cook at a simmer until the rice and peas are tender, about 1 hour.
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 3/4 cup of the breadcrumbs. Season, to taste, with salt and freshly ground pepper. Refrigerate for 30 minutes.
Shape the mixture into patties and dredge each side in the remaining 1/4 cup breadcrumbs. Heat the remaining 1 tablespoon of olive oil in a medium saute pan over medium heat. Add 2 burgers at a time and saute until brown, 3 to 4 minutes per side. To grill, cook on high for 3 to 4 minutes per side. Serve immediately.