How to complain about misconduct by passport control in Germany?

Two possibilities:

If both flights were under the same ticket, the airline needs to find you an alternative flight. It's their responsibility too take you to your destination. Airlines sometimes sell tight connections, and they know that occasionally people will miss their plane and take the next one. Happened to me twice. You should have contacted the airline representative at the airport. If they refused to help, contact their complaints department.

If you booked your flights separately, the blame is entirely on you. When planning a connection you should prepare for delays - flight delays, long queues or extra scrutiny. I wouldn't risk such a connection if it's less than several hours, even a day.

Anyway, the immigration officer just did their job, which is to verify that your documents are in order. I have no idea what made them suspicious, but it's their job to resolve such suspicions, even if it takes time.

Your choices for registering a complaint are:

• the e-mail address you received
• finding a phone number on the Federal Police's website
• finding the street address and sending your complaint in via snail mail

The most effective way is probably by e-mail or phone. E-mail wins points by being very easy to do while on the phone you can rest assured that you were heard and maybe even understood.

As for consequences, don't get your hopes high. A supervisor might talk to the agent on duty about their suspicion and conduct. The agent will most likely have a compelling reply. There will likely be no further consequences. Most notably, there will absolutely be no consequences that you as a traveller will feel – unless if you're very unlucky and Munich Airport Federal Police flag you as someone needing extra scrutiny when passing through passport control. (I don't assume that'll happen; too many people pass through every day in normal times.)

Complaining is a very German thing to do so they will certainly have a procedure to deal with it, even if that procedure is filing it under D for deleted.

What would be the most effective way of complaining?

What's the point? What are you hoping to achieve with complaining?

Don't complain. Just let it go. You're wasting your time and the time of the people handling complaints. You were allowed to transit, and you reached your destination, just with a delay. There is nothing good that you can achieve with complaining. They're not going to give you a Starbucks voucher for the inconvenience. If you had been held for three days and your rights had been violated, you would have grounds to complain. For a 15-minute delay, you do not.

I agree with many of the comments that you should plan on spending 15 minutes in immigration control. Compared to some stories from the American CBP, this sounds harmless. The German officer presumably knows US passports, his or her job is to tell the real thing from a good fake.

• You can file a criminal complaint with the prosecutor if you believe that the officer acted criminally. You do not have to know the name of the officer to do that, but a simple "someone at Munich airport took too long" might quickly be closed as impossible to resolve.
• You can file a formal complaint with the police if you believe that the officer acted unprofessionally. This should be done in writing and it would be routed to the superior of the officer, who gets to fill out paperwork and might take that unhappiness to the officer in question. The German term is Dienstaufsichtsbeschwerde, presumably you can find someone in Switzerland to help you with the letter. Again there would be the question if you can specify who and when, exactly.
• There is a web form for complaints.

And finally, the words of the other officer might simply be using de-escalation in an encounter with an agitated member of the public, rather than a professional assessment of the performance of a colleague.