Spread cream cheese on one side of each slice of bread.
Place slices of Fontina and white cheddar cheeses on one slice of bread per sandwich (~2 slices of each cheese). Place cooked bacon in between cheeses.
Make tomato soup in a small pan on the stove top according to can instructions using the milk in place of water. Let it heat up while the grilled cheese is being made.
Preheat skillet over medium heat. Rub a stick of butter all over the pan.
Set each sandwich down on the skillet. Place a lid over to trap the heat.
After a few minutes, flip the sandwiches over (coat the pan in more butter if needed). Once each side is lightly browned, add the Italian blend cheese on top, then flip them over.
At this time, turn off the burner and remove the pan from the heat. Let sit a few minutes until the cheese golden crusted.