Sounds like it could be a problem with the brake booster/servo, or the vacuum supply to it.

From the old days (not specific to BMW vehicles): Check it by confirming pedal position with the engine stopped and running.

First, turn the engine off. Pump the brake pedal until all the vacuum is gone. It will be hard. Start the engine. The pedal should drop due to the vacuum assist.

Start the engine and run it for a few minutes. Turn it off. Press the pedal several times. The pedal should come up each time; if so, the booster doesn't have a leak.

If you are checking for a vacuum leak, it is like tracking down any other vacuum leak, it will affect the idle. There will be a check valve in the vacuum line to the booster to check as well.

There are more specific tests for proper booster operation, but the above steps should point you in the right direction.

Good luck.

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