Usage of butter and flour mixture in cooking

Question

Consider this recipe and this one. In both butter and flour is mixed before cream is added. What is the idea behind mixing flour and butter?

Here are quotes of the relevant parts (in case of link rot):

1.Meanwhile, in a large cast-iron or other heavy skillet, melt butter over medium heat. Stir in flour until smooth; gradually whisk in cream. Bring to a boil, stirring constantly. Cook and stir until thickened, about 2 minutes. Reduce heat; stir in cheese until melted.

In a saucepan, melt butter over medium heat. Stir in the flour and salt until smooth. Gradually add milk. Bring to a boil; cook and stir until thickened, about 2 minutes. Stir in cheese. Pour over meat mixture; mix well. Reduce heat; cook, covered, until heated through. If desired, serve with biscuits.

From first and second recipes respectively

Answer 1

This is called a roux, a common way to thicken sauces; there is nothing about it that is specific to cast iron pans. By first cooking the flour in butter (or another fat), the taste improves and the grains of flour are coated in fat so that they do not clump together when the rest of the liquid is added.