Mix eggs, carrots, cilantro, and chickpea flour in a large bowl (mixture will be loose); season with kosher salt and pepper. Heat 2 tablespoons oil in a large skillet, preferably cast iron, over medium-high heat. Scoop two 1/2-cupfuls of carrot mixture into skillet, pressing each to 1/2″ thickness. Cook, rotating skillet occasionally for even browning, until pancakes are golden brown, about 3 minutes per side. Transfer to paper towels to drain. Repeat to make 2 more pancakes, adding more oil to skillet if needed. Meanwhile, season yogurt with kosher salt and pepper. Toss greens with lemon juice and remaining 1 tablespoon oil; season with kosher salt and pepper. Serve carrot pancakes with salad and salted yogurt, seasoned with sea salt and more pepper.