Comment by Zak

The brand name that comes to mind is the Wicked Lasers Flashtorch, which uses a 65W halogen bulb that emits most of its energy as infrared, and a ~30 Watt-hour Li-ion battery. The old-fashioned light source is better suited to party tricks than illumination.

More modern, and also capable of improvised cooking are handheld searchlights from Acebeam and Imalent with many large LEDs, cooling fans, and even bigger Li-ion batteries. There are third-party videos of these and the older halogen type cooking eggs and setting fire to paper on Youtube.

What you're describing from the ads obviously violates the laws of physics. An alkaline AA would have a hard time cooking an egg on a dead short.