Put butter in a microwave-safe container and heat for 25 seconds or until the butter is melted.
Add the EVOO to the melted butter and mix well. 
Place a large cast-iron or non-stick skillet over med-low heat.
Using a small baker's brush, coat both sides of two slices of bread and place them in the skillet.
Cook until the bottom is just starting to brown.
Flip the slices of bread over, and working quickly, evenly spread a tablespoon of pesto on one slice of bread, then sprinkle on two tablespoons of shredded mozzarella cheese.
Add four slices of pepperoni, an equal quantity of shaved ham, add more cheese and place the other slice of lightly toasted bread on top. Flip the sandwich over and finish cooking until the bread is golden brown on both sides.
Serve with small bowls of marinara sauce.