1. Preheat oven to 375°. Cook pasta according to package directions, adding broccoli during last 2 to 3 minutes of cook time.
2. Meanwhile, gradually whisk milk into flour in a bowl until smooth. Sauté shallots in hot oil in a Dutch oven over medium-high heat 1 to 2 minutes or until tender. Add wine, and cook 3 to 4 minutes or until reduced by half. Add milk mixture, and cook, whisking constantly, 7 to 8 minutes or until thickened and bubbly. Whisk in Parmesan cheese and next 3 ingredients until blended.
3. Drain pasta mixture well. Remove shallot mixture from heat, and stir in chicken, and hot cooked pasta mixture. Spoon into a lightly greased 13- x 9-inch baking dish; sprinkle with Cheddar cheese. Place dish on an aluminum foil-lined baking sheet.
4. Bake at 375° for 30 to 35 minutes or until golden brown and bubbly.