To prepare the Hogao, heat olive oil in a medium-sized pan over medium heat. Add the diced tomatoes, chopped onion, and minced garlic. Cook until the vegetables are soft and fragrant, about 8 minutes.

Add the ground cumin and salt to the Hogao, stirring well to combine. Continue cooking the sauce on low heat for another 5 minutes, allowing the flavors to meld together. Set aside.

For the veggie burger patties, in a large bowl, mash the black beans using a fork or potato masher until they're mostly smooth, leaving some texture. Add cooked brown rice, breadcrumbs, soy sauce, smoked paprika, and black pepper. Mix until well combined.

Shape the bean mixture into four equal-sized patties. Heat a skillet or griddle over medium-high heat. Cook each patty for about 5 minutes on each side, or until they develop a golden-brown crust.

To assemble the burgers, place a lettuce leaf on the bottom half of each toasted bun. Top with a veggie patty, a generous spoonful of Hogao, and sliced avocado. Crown with the top bun and serve immediately.