For the apple-mascarpone cream: Combine the apples, sugar, cinnamon and 1/2 cup water in a small saucepan. Bring to a simmer, cover and cook over low heat, stirring occasionally, until the apples are completely tender, about 12 minutes. Uncover and cook, stirring, until reduced to the consistency of applesauce, about 2 minutes. Transfer to a bowl and cool completely. Once cool, combine 1/2 cup of the applesauce with the mascarpone; mix to blend. Refrigerate until ready to serve. (Reserve extra applesauce for another use.)
For the apple-berry compote: Combine the apple cider and sugar in a medium saucepan. Bring to a boil, then reduce to a simmer and cook until syrupy, about 10 minutes. Cool until warm. Add the strawberries, blackberries and blueberries to the syrup. Keep warm until ready to serve. (This makes more compote than you'll need, but it's a delicious topping for ice cream!)
For the French toast: Preheat a grill pan to medium low. In a medium bowl, combine the eggs, sugar, vanilla and cinnamon. Then whisk in the milk. Brush the hot grill pan with butter to coat.
Dip 3 brioche slices into the egg mixture; flip and dip on the reverse side. Remove from the egg mixture, letting any excess fall back into the bowl. Immediately add the bread to the grill pan. Cook until crisp and grill marks appear, 1 to 2 minutes. Flip and cook until cooked through, 3 minutes more. Remove to a plate and keep warm. Repeat with the remaining 3 brioche slices.
To serve, add 3 slices of French toast to each plate. Top with apple-berry compote and dollop some apple-mascarpone cream on the side.