01 -
Bring a large pot of salted water to a boil. Add pasta shells and cook until al dente according to package directions. Drain thoroughly and set aside.
02 -
In a large cast iron skillet over medium-high heat, melt butter. Add minced garlic and shallot, stirring frequently, and sauté until fragrant, about 2 minutes.
03 -
Sprinkle flour over the aromatics and whisk constantly until the mixture is lightly browned, approximately 1 minute.
04 -
Gradually whisk in whole milk, half and half, and Dijon mustard. Continue to cook, whisking, until slightly thickened, 3 to 4 minutes. Adjust consistency with additional milk if needed. Season with kosher salt and pepper to taste.
05 -
Stir in drained pasta, chopped broccoli, and grated cheddar cheese. Cook, stirring gently, until cheese is melted and ingredients are evenly incorporated, 3 to 4 minutes.
06 -
Transfer to serving bowls and serve immediately while hot.