In a small bowl, whisk together the eggs, milk, and granulated sugar. Spread the cream cheese on half of the bread slices and top with strawberries. Top with the remaining 6 bread slices and press around the edges to seal.
Melt butter on a griddle over medium-low heat. Dip the sandwiches in the egg mixture for a few seconds on each side. Cook the sandwiches until golden brown, 2 to 3 minutes per side. Serve with maple syrup, Strawberry Syrup, or confectioners' sugar.
In a medium saucepan, combine all the ingredients and bring to a boil. Lower the heat and simmer until the strawberries are soft and the syrup is thickened and reduced by 1/3 to 1/2 in volume, 15 to 18 minutes.
Remove from the heat and let cool to room temperature before serving.
If a thinner syrup is desired, strain the hot syrup through a fine mesh strainer into a clean container and let cool.