Place shredded potatoes in a microwave-safe bowl and microwave for 3 minutes. While potatoes are heating, pour 3 tablespoons vegetable oil into a 12-inch cast-iron or nonstick skillet. Heat the oil over medium to medium-high heat.
Remove the potatoes from the microwave and spoon 1 cup of the potatoes into the skillet. Repeat with another cup of potatoes and flatten each mound of potatoes to make a patty. Cook hash browns for 5 minutes.
While hash browns are cooking, drain and rinse the beans. Combine beans with a large handful of cilantro, lime juice, cumin, garlic paste, cayenne, and salt in the bowl of a mini food processor. Process until smooth. Set aside.
Turn the potato patties over and cook for another 5 minutes, until they are lightly browned. Dice the avocado and slice the green onions.
Remove the patties from the pan. Add the remaining 3 tablespoons oil to the pan and repeat with the remaining potatoes.
Spread 2 tablespoons of the black bean mixture on each patty and top with romaine, salsa, cheese, avocado, green onions and sour cream (if using).