Grease a shallow 1-quart baking dish. Place the torn croissant pieces in the bottom of the dish in an even layer.

Prepare the caramel sauce by placing a medium saucepan over medium-low to medium heat. Add butter and allow to melt. Mix in brown sugar and stir for 2 minutes. Mix in heavy cream and stir for 2 more minutes. Remove pan from heat and stir in vanilla and salt until well incorporated. Allow to cool for 5 minutes.

Preheat oven to 350°F. In a medium bowl, whisk eggs. Very slowly and gradually, pour in the slightly cooled caramel sauce, rapidly whisking the whole time. (If the caramel sauce is too hot, or if you pour it in all at once, or if you're whisking too slowly, the eggs may scramble, which is not what you're going for!)

Pour caramel sauce mixture over croissant pieces. Press down on croissants so that all of them are submerged in caramel sauce and allow to rest for 10 minutes. Bake for 20 minutes; remove to a rack and cool for 10 minutes. Serve warm.