Preheat oven to 400 degrees. Place the milk and cream in a saucepan over medium heat and cook until just boiling.
Remove the pan from the heat and set it aside. Place the egg yolks, sugar, and vanilla in a bowl and whisk to combine. Gradually whisk the warm milk mixture into the egg mixture to combine the two.
Arrange the brioche slices in the base of a lightly greased 8-inch baking dish. Pour the custard over the brioche and top with the currants and strawberries.
Sprinkle with the sugar and bake for 20–25 minutes or until golden.