Place 2 slices of bread onto a work surface.
Spread 1 tablespoon of peanut butter on one slice and spread condensed milk on the other slice of bread.
Close the sandwich with the fillings enclosed.
In a large shallow bowl, beat together the eggs, milk, melted butter, and vanilla extract until incorporated.
Preheat a frying pan over medium heat.
Dip the sandwich into the egg mixture, and flip it over so both sides are covered with the custard. Be careful not to oversoak the bread.
Add 1 teaspoon of butter to the pan and give it a swirl.
Place the sandwich into the pan and cover with a lid. Cook for 2-3 minutes on medium-low heat.
Flip the sandwich and cook for another 2 minutes, until golden in colour.
Remove from the pan and repeat with the remaining sandwiches.
Serve immediately with extra condensed milk and a pat of butter.