Preheat the oven to 350 degrees F (175 degrees C). Spray muffin cups or brownie pan with cooking spray.

Mix milk, cream, eggs, sugar, and vanilla extract together in a bowl. Scrape the insides from each vanilla bean half into the milk mixture. Stir milk mixture until smooth and light yellow in color. Carefully stir croissant pieces into milk mixture until all the pieces are wet; let soak for at least 10 minutes.

Fold chocolate chips into croissant mixture. Spoon croissant mixture into the prepared muffin cups or pan.

Bake in the preheated oven until bubbling and golden brown, 35 to 45 minutes. Cool pudding for 30 minutes to 1 hour; transfer to a plate and dust with confectioners' sugar.