Preheat the oven to 425° F. Place the slices of bread on a baking sheet. Bake for 10 minutes until they begin to look toasted. Take the bread out and set aside. Turn the oven to broil on high.
In a food processor combine the white cheddar cheese, mozzarella cheese, egg, butter, dijon mustard, and pepper. Blend until the cheese mixture is fully combined into a smooth spread. Transfer to a bowl and set aside.
Drizzle the bread slices in red wine, about 1 oz per slice or as needed. Allow the wine to soak into the bread. Spread a thick layer of the cheese spread over the wine-soaked toast. Broil on high for 3 to 4 minutes, watching closely, until the cheese is melted, bubbling, and just beginning to brown. Serve and enjoy!