In a medium saucepan, add the coconut milk, ginger, 1 tablespoon salt and 2 cups water. Bring to a boil over medium-high heat. Add the orzo and stir. Cook, stirring to prevent sticking, until the pasta is al dente, 6 to 7 minutes. Drain well. Remove and discard the ginger.
Heat a large skillet over medium-high heat. Add 2 tablespoons of the oil and heat for 1 minute more. Add the drained orzo and spread out evenly in the skillet. Cook, undisturbed, until the bottom of the pasta is starting to get browned and crispy, about 4 minutes. Flip the pasta, add the remaining 2 tablespoons oil and continue to cook, undisturbed, until the other side is browned, about 4 minutes more. Flip again and brown another 3 minutes. Season with 1/4 teaspoon salt and stir in the peas and scallions. Cook another 2 minutes to warm through. Finish with the lemon juice. Serve warm.