In a large saucepan of boiling, salted water, cook the tortellini until al dente; drain.
Meanwhile, add the peas, butter and scallion whites to another large saucepan and cook over medium heat for 2 minutes. Whisk in the flour and cook, stirring, for 1 minute. Gradually whisk in the milk and bring to a boil, stirring constantly. Stir in the scallion greens and season with salt and pepper.
Stir the tortellini and 1/3 cup cheese into the sauce. Divide the pasta among 4 serving bowls and Easy does it sprinkle with more cheese.