Whisk together the eggs, milk, cream, vanilla and cinnamon. Lay the brioche slices in a single layer in a shallow dish and pour the egg mixture over them. Allow to soak for 2-3 mins, then carefully turn over and soak for 2 mins more.
Heat 1 tbsp of the vegetable oil and butter in a non-stick frying pan over a medium heat until foaming. Carefully lift 2 slices of the soaked brioche out of the dish and add to the frying pan. Fry for 3 mins on each side, until golden and crisp, then place on a wire rack over a baking tray in a warm oven while you repeat with the remaining slices.
Serve dusted in icing sugar and scattered with fresh berries, if you like.