Place each slice of bread on a flat surface and use a rolling pin to flatten it completely.
Sprinkle shredded cheese evenly over each slice of bread. Add ham if using.
Roll the bread tightly from one end to the other, pressing gently to seal the edge.
Heat a nonstick skillet over medium heat and melt butter.
Place grilled cheese roll ups seam-side down in the skillet.
Cook for 4 to 6 minutes, turning occasionally, until all sides are golden brown and crispy.
Remove from heat and serve warm with your favorite dipping sauce.