In a medium bowl, whisk together the whole eggs, egg yolks, half-and-half, sugar, and vanilla. Set the custard mixture aside. Slice the croissants in half horizontally. In a 10 by 15 by 2 1/2-inch oval baking dish, distribute the bottoms of the sliced croissants, then add the chocolate chips, then the tops of the croissants (brown side up), being sure the chocolate chips are between the layers of croissants or they will burn while baking. Pour the custard over the croissants and allow to soak for 10 minutes, pressing down gently.
Place the pan in a larger one filled with 1-inch of hot water. Cover the larger pan with aluminum foil, tenting the foil so it doesn't touch the pudding. Cut a few holes in the foil to allow steam to escape. Bake for 45 minutes. Uncover and bake for 40 to 45 more minutes or until the pudding puffs up and the custard is set. Remove from the oven and cool slightly. Serve warm or at room temperature.