Fill a large pot with water, add salt, and bring it to a rolling boil.

Add the pasta shells and cook according to the package instructions until al dente.

During the last 2 minutes of cooking, add the chopped broccoli florets to the boiling water with the pasta.

Using the same pot, heat the butter over medium heat until it melts.

Add the minced garlic and shallot, cooking for 1-2 minutes until fragrant and softened.

Stir in the flour and cook for 1-2 minutes to form a roux, stirring constantly.

Gradually whisk in the whole milk and half and half, making sure the mixture stays smooth.

Add the Dijon mustard, then season with kosher salt and freshly ground black pepper to taste.

Bring the mixture to a gentle simmer and cook for about 3-5 minutes, stirring occasionally, until the sauce thickens slightly.

Remove the sauce from heat and gradually stir in the grated cheddar cheese, one handful at a time, until completely melted and smooth.

Add the cooked pasta and broccoli back into the pot with the cheese sauce. Stir until everything is well combined and the pasta and broccoli are evenly coated with the sauce.

Serve the creamy broccoli mac and cheese warm, garnished with extra grated cheddar or a sprinkle of freshly ground black pepper if desired.