Preheat oven to 375°.
Combine first 6 ingredients in a large bowl. Sprinkle with 1/2 teaspoon salt and pepper; toss to combine.
Layer one-third of potato slices in a 13 x 9-inch baking dish coated with cooking spray, overlapping to fit; top with half of broccoli mixture. Repeat layers, ending with potato. Sprinkle evenly with remaining 1/4 teaspoon salt.
Place 3 tablespoons flour in a medium bowl. Gradually add milk, stirring constantly with a whisk; stir in broth. Pour milk mixture over potato mixture. Top evenly with butter. Cover and bake at 375° for 1 hour. Uncover; sprinkle evenly with cheese. Bake 25 minutes or until browned. Cool on a wire rack 10 minutes.