Preheat your oven to 350°F / 175°C.
Tear the stale croissants into bite-sized pieces and arrange them in a small gratin dish or two individual ramekins (approximately a 2-cup capacity).
In a small saucepan, combine the sugar and water. Swirl the pan gently to moisten the sugar, then place it over medium-high heat.
Let the mixture bubble away without stirring for 3-5 minutes. Watch it closely until it transforms into a deep amber-colored caramel.
Don't be afraid to let it get dark for a richer flavor, but don't let it burn.
Immediately reduce the heat to low and carefully pour in the heavy cream. The mixture will sputter and seize—this is normal!
Whisk continuously as you add the milk and bourbon.
Keep whisking over low heat until any hardened caramel has completely dissolved into a smooth sauce.
Remove the saucepan from the heat.
While whisking constantly, slowly pour in the beaten eggs until fully incorporated. This tempers the eggs and prevents them from scrambling.
Pour the warm caramel-bourbon custard evenly over the croissant pieces. If your croissants are very dry, let the pudding sit for 10-15 minutes to allow them to soak up the liquid.
Bake for 20 minutes, or until the custard is set but still has a slight wobble in the center.
Remove from the oven, let it cool for a moment, and prepare to swoon.
When adding the cream to the hot caramel, it will bubble and seize violently. Stand back and add it slowly and carefully.
Keep whisking, and any hardened caramel will melt back into the sauce.
