Preheat the oven to 350 degrees F. Lightly butter a 9-inch baking dish.
In a large skillet, melt the butter over medium heat. Add the carrots and scallions and cook for 6 minutes, stirring occasionally.
Stir in the flour, parsley, salt and pepper and cook for 2 minutes, stirring occasionally. Add the milk and cook until thickened, 2 to 3 minutes. Stir in the cheese. Spoon the mixture into the prepared baking dish. Top with the chips. Bake until hot and bubbly, about 30 minutes.