Preheat the oven to 350 degrees.
Generously spray a 9X11 baking dish.
Melt 3 Tablespoons of butter in a large pot. (I use a dutch oven.) Add the chopped onion and fry until it is softened.
Whisk in the flour, salt, and pepper. Cook this for at least 3 minutes or until it is bubbly.
Add the milk and cream. Stirring constantly, cook this until it boils and thickens.
Stir in the cheese and cook until melted.
Stir in the carrots and parsley. Spread this mixture into the prepared baking dish.
In a medium bowl, melt 2 Tablespoons of butter and stir in the cornflakes until coated.
Sprinkle the cornflake mixture evenly over the top of the carrots.
Bake for 20 minutes, then serve.