In a large bowl, mix together shrimp, carrots, cilantro, 2 teaspoons soy sauce, green onions, eggs, and 3/4 cup water. Add flour and stir until combined. Oil a large skillet generously and heat over medium-high heat. Working in batches, use about 2 tablespoons of the shrimp mixture to form each pancake, spreading it out into a 2-inch round. Cook, flipping once, until deep golden brown and cooked through, 6 to 8 minutes.
Place finished pancakes on a rack on a large sheet tray in a 250 degree oven to keep them warm as you go. Meanwhile, toss satsumas with remaining 1 teaspoon soy sauce. Top pancakes with relish and serve immediately.