Make the filling: In a large bowl, use a spatula to combine the cream cheese, powdered sugar, and the vanilla extract. Mix together until fluffy and smooth.
Lay out a piece of plastic wrap and arrange 4 rows of 2 whole slices of brioche bread. Cut 2 pieces of brioche bread in half and add to the end of each row.
Beat 1 egg in a small bowl. Brush egg wash on the left side of each piece of bread, except for the farthest left pieces in each row. Overlap the right edges over the egg wash and press to adhere. Brush egg was along the bottom of each row of bread, except for the bottom row. Overlap the top edges of each row over the egg wash and press to adhere.
Use a spatula to spread an even layer of the filling over the bread. Distribute the strawberries over the filling.
Using the plastic wrap for help, roll up the bread. Twist the ends of the plastic to seal.
Freeze for 1 hour.
In a medium bowl, whisk together the remaining 3 eggs, the milk, sugar, and cinnamon.
Preheat the oven to 425°F (220°C).
Remove the roll from the freezer. Remove plastic wrap and transfer to a greased baking sheet. Brush all over with the cinnamon egg mixture.
Bake for 12 minutes, or until golden brown.
Remove from oven. Dust with powdered sugar, slice, and serve with a drizzle of maple syrup.