Arrange broccoli and carrot in a steamer basket over boiling water. Cover and steam 3 minutes or until crisp-tender.
Combine flour and 1/4 cup milk; stir until smooth. Combine flour mixture, remaining 1 1/4 cups milk, broth, wine, and margarine in a medium saucepan. Cook over medium heat, stirring constantly with a wire whisk, until mixture is thickened and bubbly. Remove from heat; stir in sour cream, lemon juice, ground pepper, and salt. Add steamed vegetables, chicken, and mushrooms; stir well. Spoon mixture into an 11- x 7- x 1 1/2-inch baking dish coated with cooking spray. Cover and bake at 325° for 35 minutes. Uncover, sprinkle with Cheddar cheese, and bake 5 additional minutes or until cheese melts.
To serve, place 1 wedge of Skillet Cornbread on each plate. Spoon chicken mixture evenly over cornbread wedges.