If you find no vacuum leak, then I would replace the brake booster because what is happening when you press the brakes hard is basically causing the engine vacuum to drop too low and this will stall the engine.
I am attaching the info below that will help with doing this.
Please run through this information and let me know what questions you have.
Repair Safety Notice: This information is for general instructional purposes only. Vehicle repair can be dangerous. Verify all information, follow manufacturer service procedures, use proper tools and safety equipment, and consult a qualified repair shop when needed.