More than likely you have a vacuum leak either in the intake or the brake booster that we need to find.
Here is a guide that will help with this:
https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge
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.
Thanks
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Thursday, December 16th, 2021 AT 7:53 AM