Cook beans: Place the 1 cup black beans in a large saucepan and cover them by a couple inches of water. Add a good 5-finger pinch of salt and bring to a boil, then reduce heat to low and simmer until tender, about an hour. Remove from heat.
Make salsa and slaw: Meanwhile, stir together the pico de gallo and cilantro-lime slaw.
Cook farro: In a separate medium saucepan, heat 1 tablespoon of the olive oil over medium heat. Add the 1/3 cup farro and toast, stirring constantly, until it starts to brown, about 2 minutes. Cover with water by a couple inches and season with salt. Simmer until grains have begun to pop open and are tender, about 30 minutes. Remove from heat.
Sauté the aromatics: Heat 2 tablespoons of the oil in a medium frying pan over medium heat. Add onions and garlic and season with salt and pepper. Cook until tender and starting to brown. Remove from heat.
Blend: Drain the beans and place half in the bowl of a food processor fitted with the blade attachment. Pulse to break up the beans but not too small. Transfer to a large bowl. Drain farro and add to the food processor along with the remaining beans, onion mixture, 2 eggs, 1 cup bread crumbs, 1 teaspoon of salt, 1 teaspoon thyme leaves, and 1/4 cup chopped cilantro. Pulse into a chunky puree and add to the bowl with the other black beans. Mix together with your hands until combined.
Form into patties: Form the mixture into 8 large patties (about 1/2 cup each), cover and refrigerate for at least 30 minutes or up to 1 day.
Pan-fry cakes: Heat 1 1/2 tablespoons of the olive oil in a large nonstick frying pan over medium heat. Add half of the cakes and fry on one side until browned and crispy, about 4-5 minutes. Flip and repeat on the other side. Remove from pan and add remaining 1 1/2 tablespoons oil to pan. Add remaining black bean cakes and fry until browned and crispy on both sides.
Serve: Nestle black bean cakes on a bed of slaw on each plate and top with the pico de gallo. Enjoy!