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 tb 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 other 1 tb of butter, oil and garlic, cook only until butter is melted
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 shells, broccoli, and chicken and mix until fully incorporated
ENJOY!