Preheat the oven to 350 degrees F.

In a small saucepan, add the carrots, 1/2 teaspoon salt and water. Over medium high heat, bring to a boil, cover and reduce to a simmer until the carrots are soft, about 20 minutes. Transfer the carrots to a blender or food processor and puree.

In a large saucepan of salted boiling water, cook the penne until al dente according to package instructions. Drain the pasta reserving 1 cup of the cooking water.

Return the pasta to the pot and stir in the carrot puree and cooking water. Over medium heat, cook, stirring frequently, until the sauce has thickened. Stir in the remaining salt and about three-fourths of the cheese until melted. Transfer to a square baking dish and top with the remaining cheese and sprinkle with breadcrumbs. Bake for 20 minutes until the cheese has melted and the top is lightly browned. Let the mac & cheese stand for 5 minutes before serving. Sprinkle with chives.