In a large pot of boiling salted water, add the pasta shells and cook according to the package instructions, usually around 8-10 minutes. Drain and set aside.

In a large cast iron skillet over medium-high heat, melt the butter. Add minced garlic and shallot, sauté for about 2 minutes until fragrant.

Whisk in the flour into the buttery mixture, cooking for about 1 minute. Gradually pour in the whole milk and half and half while whisking to prevent lumps. Cook until the sauce thickens, about 3-4 minutes.

Add the chopped broccoli florets to the sauce and cook for an additional 3-4 minutes until the broccoli is tender.

Gently fold in the cooked pasta and grated cheddar cheese until combined and the cheese melts, about another 3-4 minutes.

Remove from heat and serve immediately.