Preheat oven to 350°F. Grease a 9x13 baking dish with butter or cooking spray and set aside.
To make the cookie dough, in a medium bowl, cream together the butter, brown sugar, granulated sugar, and vanilla until thick and fluffy. Stir in the flour and salt until just combined. Fold in the chocolate chips and set aside.
In a large bowl or large measuring cup with a spout, whisk together the milk, cream, eggs and vanilla until well combined.
Lay half of the brioche slices in an even layer on the bottom of your prepared baking dish. Sprinkle with half of the cookie dough, breaking off small pieces in varying sizes. Repeat with the remaining brioche slices and the rest of the cookie dough. Carefully pour the custard mixture over the bread, using all of it. Allow to sit for 20 minutes to soak up the liquid as much as possible.
Bake until the custard has set and the pudding is golden brown, about 45 to 50 minutes. Remove from the oven and allow to cool for 10 minutes before serving. Serve with a dusting of powdered sugar and a dollop of fresh whipped cream or a scoop of vanilla ice cream. Leftovers can be kept in the fridge for up to 3 days and rewarmed in the oven. Enjoy!