Cheesy Chicken & Broccoli Pasta

8 ounces pasta, uncooked (shells are an excellent choice)
1 pound of chicken, cubed (no skin) COOKED
2 cups broccoli fresh or frozen
3 tablespoons olive oil
2 tablespoons butter
1 teaspoon black pepper
1 cup shredded cheese of your choice
3 cloves of garlic, minced
1 cup heavy cream
1/4 cup whole milk
1 cup broth, beef or chicken
1/4 cup all-purpose flour
1 teaspoon Cajun seasoning or chili powder
1 teaspoon of salt to taste

In a medium pot, boil the broccoli until softened and set aside
Boil a large pot of lightly salted water and add pasta , then drain
Add pasta back into the hot/empty pot and add 1 Tbs of butter, stir until fully melted and pour into a large bowl and set aside while we make the sauce.

In the same pot, add in the 2 Tbs of butter and melt
Once melted, whisk in the flour and cook while stirring constantly, then add in the heavy cream, milk and all other seasonings, continuing to stir the whole time while bringing to a low boil
Add in the cooked pasta (yes, still recommend shells), broccoli, and chicken and mix until fully incorporated.