In a large pot, boil water and add a pinch of salt. Once boiling, add the elbow macaroni and cook until al dente, adding the broccoli florets a minute or two before the pasta finishes.

Drain the pasta and broccoli and set aside.

In the same pot, melt the butter over medium heat. Sprinkle in the flour, whisking continuously for about a minute until it becomes a light golden color.

Gradually whisk in the milk, ensuring there are no lumps. Bring to a gentle simmer, stirring constantly until it thickens, about 5-7 minutes.

Remove from heat and gradually add in the shredded cheddar cheese, stirring until fully melted. Season with salt and pepper to taste.

Gently fold in the drained pasta and broccoli until everything is well coated with the cheese sauce.

Transfer to a serving dish, optionally sprinkle extra cheese or breadcrumbs on top, and serve hot.