Place the strawberries in a container with a lid, and sprinkle 1 teaspoon sugar over. Add the lid and shake. Let sit while you prepare the other ingredients.
Pour the cream cheese, mascarpone, 2 tablespoons sugar, and ¼ teaspoon vanilla into a bowl of an electric mixer. Whip the ingredients together on a medium speed for 1 minute, until slightly fluffy. Scrape down the side of the bowl if necessary.
Whisk the eggs, milk, remaining vanilla, and remaining sugar together in a shallow bowl.
Melt 1 teaspoon butter in a skillet over medium heat.
Dunk the brioche in the egg mixture, soaking each side of the bread completely.
Place the bread in the skillet and toast until brown. This will take 2-3 minutes. Then add the remaining butter, and flip the bread. Toast until golden brown.
Remove the french toast from the skillet, and spread the nutella on one slice, and top with the strawberries. Spread a thick layer of the cheesecake filling over the other slice of bread, and stack on top of the strawberries to create a sandwich.