Preheat oven to 350 degrees F. Line an 8x8 inch baking dish with parchment paper or spray well with cooking spray.
In a medium-sized bowl, whisk together the eggs, egg whites, milk, salt and pepper.
Pour mixture into the prepared baking dish. Bake for 15 minutes or until egg mixture has cooked through and is no longer runny.
Once egg mixture has baked, allow it to cool for several minutes.
Remove the egg mixture from the pan and cut into four squares of equal size or use a circular cookie cutter or the lid of a mason jar to cut out four circles from the egg mixture.
Place each egg square or circle on the four English muffin halves and spread one tablespoon of pesto evenly over top of each egg. Evenly divide the shredded cheese among the breakfast sandwiches. Top with other English muffin half and bake immediately or place in fridge or freezer for later use.
If serving right away, place in oven at 350 degrees F for 5-10 minutes or until cheese has melted and English muffin is slightly crispy. If freezing for later, do not heat the breakfast sandwiches. Instead, wrap them in parchment or wax paper and place them in a resealable freezer bag. Freeze for up to 1 month.