In a small bowl, dissolve the cornstarch in the water and set aside.
In a large saucepan, melt the butter. Add the flour and cook, stirring regularly, for about 5 minutes.
Add the beef and chicken broth & bring to a boil, stirring with a whisk.
Stir in 1 tbsp of the cornstarch mixture and simmer for a minute or so. If you'd like your gravy thicker, slowly add more of the cornstarch mixture, in small increments, as needed. Season with pepper. Taste, and add additional salt if necessary, to taste. Make ahead & re-warm or keep warm until your fries are ready.