In a saucepan on medium heat bring the chicken broth to a simmer.
In a bowl whisk the flour and water together until the flour dissolves completely and there are no lumps. Pour the mixture into the simmering broth; continue simmering until the broth thickens.
Add the turkey to the gravy and continue simmering for 4 - 5 minutes.
Melt the cheese on the rolls underneath the broiler.
Place the turkey onto the roll, drizzle with gravy, cut in half, and serve with chips and pickles on the side.