Preheat oven to 400°. Prepare cellentani pasta according to package directions.
Meanwhile, melt 3 Tbsp. butter in a Dutch oven over medium heat. Gradually whisk in flour; cook, whisking constantly, 1 minute. Gradually whisk in milk until smooth; cook, whisking constantly, 8 to 10 minutes or until slightly thickened. Whisk in 1 cup sharp Cheddar cheese and next 3 ingredients until smooth. Remove from heat, and stir in ham, vegetables, and hot cooked pasta.
Spoon pasta mixture into a lightly greased 13- x 9-inch baking dish. Stir together crushed cracker crumbs and 2 Tbsp. melted butter; sprinkle over pasta mixture.
Bake at 400° for 25 to 30 minutes or until golden and bubbly. Let stand 5 minutes before serving.
