Place the stick of butter in a large saucepan and sprinkle the black pepper on top. Melt over medium-low heat, stirring occasionally so it does not scorch and the pepper is evenly distributed.
While the butter melts, pour the turkey drippings and juices into a liquid measuring cup. You need 2 cups total; if you are short, top off the difference with chicken broth.
Once the butter has melted completely, slowly add the flour while whisking constantly to avoid lumps. Keep stirring over medium heat for about 2 minutes, until the roux is a smooth, golden, fragrant paste.
Slowly pour the drippings into the roux while stirring. Keep stirring for several minutes as the gravy thickens. It is ready when it coats the back of a spoon. For a thinner gravy, whisk in a little extra chicken stock.
Pour into a gravy boat and serve warm. To hold it, keep the saucepan on the lowest heat setting until the rest of the meal is ready.