Separate the dark greens from the light green and white part of the scallions. Thinly slice the dark green parts at an angle until you have about ¼ cup; set aside for garnish (reserve any remaining dark green parts for another use). Chop the remaining light green and white parts.

In a medium saucepan over medium heat, heat 1 tablespoon of the oil until shimmering. Add the chopped light green and white scallions and cook, stirring occasionally, until softened, 2 to 3 minutes. Sprinkle the flour over the scallions and cook, stirring, until incorporated, about 30 seconds. Slowly add the milk to the pan, stirring constantly, and bring to a gentle simmer. Maintain the gentle simmer, stirring occasionally, until the mixture thickens slightly, about 2 minutes.

Transfer the scallion-milk mixture to a blender. Add the basil, parsley and ¼ teaspoon of salt, and blend until smooth and pale green. Return the sauce to the saucepan, set it over low heat and cook, stirring frequently, until the mixture thickens further and is the consistency of thin pancake batter, about 5 minutes. Remove from the heat and cover to keep warm. You should have about ¾ cup sauce.

Pat the scallops as dry as possible on both sides. In a large skillet over medium-high heat, heat 1 tablespoon of the oil until shimmering. Add half of the scallops and cook, without moving them, until they brown on the bottom and release easily from the pan with a metal spatula, about 2 minutes. Flip and cook until no longer translucent in the center, 1 to 2 minutes more. Transfer the cooked scallops to a plate, add the remaining 1 tablespoon of oil to the skillet and repeat with the remaining scallops. Season the cooked scallops with the lemon juice, and the remaining salt and pepper.

To serve, spread a few tablespoons of the sauce onto each serving plate. Top each with 4 scallops and garnish with the reserved scallion greens.