Tahini, soy sauce, and lime come together for a savory, umami-laden dressing that plays well with runny egg yolks. Fresh cilantro brightens things up, and chewy farro and crunchy veggies add plenty of texture to this protein-and fiber-packed bowl.
Stir together lime juice, tahini, soy sauce, sesame oil, and ginger in a medium bowl until combined and smooth. Add farro and cilantro; toss to coat.
Heat 1 tablespoon olive oil in large cast-iron skillet over medium-high until shimmering and fragrant. Crack 2 eggs into hot oil. Cook, gently tilting skillet occasionally to redistribute oil and spooning a little oil onto egg whites to gently cook, until egg edges are brown and whites are set but yolks still runny, 1 1/2 to 2 minutes. Transfer eggs to a plate lined with paper towels. Repeat with remaining 1 tablespoon oil and remaining 2 eggs.
Divide farro mixture evenly among 4 bowls. Top evenly with cucumbers, carrots, edamame, and fried eggs. Sprinkle eggs evenly with salt. Serve immediately.