Preheat the oven to 350ºF and grease a 12-inch oval baking dish with softened butter. Set aside.
Slice the brioche loaf into 1-inch thick slices and lightly toast in the oven for a couple of minutes. Remove from the oven and spread a little bit of butter on each slice. Arrange the brioche slices in the baking dish and set aside.
In a large bowl, combine whole milk, heavy cream, eggs + egg yolks and vanilla, and whisk to combine. Add the sugar, brown sugar and salt, whisking until fully incorporated.
Pour the egg mixture over the entire loaf. Tip: use a brush to coat every slice.
Bake the French toast for 20 minutes covered with foil, until egg mixture is set. Remove the foil and bake for an additional 5-10 minutes until golden.
Remove from heat and sprinkle the white and dark chocolate on top, followed by fresh raspberries and blackberries just before serving.
Serve warm with a drizzle of maple syrup, or dust powdered sugar on top!