Bring a large pot of lightly salted water to a boil. Cook broccoli and elbow macaroni in the boiling water, stirring occasionally, until pasta is tender yet firm to the bite, about 8 minutes. Drain.
Preheat oven to 375 degrees F (190 degrees C). Spray a baking dish with cooking spray.
Melt butter in a large, heavy skillet over low heat. Add onion; cook and stir until slightly softened, about 2 minutes. Add flour; cook until golden and well combined, about 1 minute. Raise heat to medium-high. Whisk in milk and chicken broth and bring to a boil. Cook and stir until sauce is smooth and thick, about 5 minutes more. Season with salt and pepper. Remove from heat.
Stir Cheddar cheese into the sauce; add the cooked broccoli and macaroni. Mix well and pour into the prepared baking dish. Top with breadcrumbs and Parmesan cheese. Spray cooking spray on top.
Bake in the preheated oven until set, 15 to 20 minutes. Place under the broiler; cook until breadcrumbs are golden, about 3 minutes more.