Preheat oven to 350 degrees.
On a lightly floured surface roll one dinner roll into a 4 inch circle. Place one to two slices of deli ham onto each circle, top with one cheese slice that has been cut in half or approx. 1/4 cup shredded cheese per roll.
Fold top half of dough over to make a half circle. Using a fork press down around the outside to seal the edges of the dough.
Repeat and assemble remaining dinner rolls. Place on a greased baking sheet about 2 inches apart and brush with egg wash.
Bake in a 350 degree oven for 15-17 minutes or until golden brown on top.