2.Whisk eggs in a large bowl until frothy. Add the rice mixture and mash with a potato masher until the mixture holds together (it will be fairly soft), about 1 minute. Shape the mixture into 8 patties.
3.Heat 2 teaspoons oil in a medium nonstick skillet over medium-high heat. Carefully transfer 4 patties to the pan with a spatula and cook until browned and crispy, about 3 minutes per side. Transfer to a plate; cover to keep warm. Wipe out the pan with a paper towel, add the remaining 2 teaspoons oil and repeat with the remaining 4 patties.
4.Meanwhile, combine beans and salsa in a small saucepan and cook over medium-high heat, stirring occasionally, until hot, about 5 minutes. To serve, divide the beans among 4 plates and top with 2 patties each.