In a large pot, melt 1 tablespoon of butter. Pour in the orzo and toast it for 3 minutes. Add 3.5 cups of chicken broth and cover the pot with a lid. Cook the orzo per instruction until al dente. Remove the pot from the heat. Open the lid and fluff the orzo.
Add the butter into the pot with the orzo. While the orzo is still hot, add in the pecorino cheese and black pepper and stir while slowing adding in as much of the ½ cup of chicken broth as necessary until the cheese has fully melted into a silky smooth sauce.
Serve with an additional sprinkle of cheese and black pepper.
Substitute the chicken broth with vegetarian broth.