Heat the oven to 350°. Spread the walnuts on a baking sheet. Toast them in the oven until they're light golden brown, about 8 minutes. Let them cool.
Make the pesto. Place the parsley, walnuts, Parmesan, scallions, and salt in a food processor and pulse until the ingredients are well blended and finely chopped. With the machine still running, slowly add the olive oil and process until the mixture forms a thick paste. Add the lemon juice and blend until it's incorporated.
Place a steam basket in a large pot with an inch of water and bring it to a boil over high heat. Steam the carrots, covered, for 3 minutes. Add the green beans, cover, and continue steaming the vegetables until they're just tender, about 4 to 5 minutes more. Transfer the vegetables to a large serving bowl.
Toss the vegetables with 1/2 cup of the pesto. If desired, adjust the seasoning with salt, pepper, and lemon juice. Serve warm with the remaining pesto on the side.