Place 1 in. of water in a saucepan; add carrots. Bring to a boil. Reduce heat. Cover and simmer for 5-8 minutes or until carrots are almost tender.
Meanwhile, in a small saucepan, saute onion in 3 teaspoons butter until tender. Stir in flour, salt and pepper until blended. Gradually whisk in milk. Bring to a boil; cook and stir 1-2 minutes or until thickened.
Remove from heat; stir in cheese and parsley until cheese is melted. Drain carrots; add to sauce.
Transfer to a greased 2-cup baking dish. Melt remaining butter; stir in cornflakes. Sprinkle over carrots. Bake, uncovered, at 350° for 15-20 minutes or until bubbly and golden brown.