2 days overdue schengen visa

You entered Schengen as a person not needing a prior visa and you want to overstay for 2 days. You listed your options as...

1. ask for an extension of leave at a border control prior to overstaying
2. overstay and see what happens

For the first option: There is a provision in Schengen for an individual to ask for an extension but success is very difficult. In your case, the officer would likely conclude that you were in a position to know your expiry date at the time you booked your flight; he would also conclude that you are in a position to be aware that spending Christmas with your bf would result in an overstay. He would combine these two facts and conclude that your overstay is avoidable and arises solely from personal convenience. So he would, in all likelihood, refuse your request for an extension.

Moreover, given that you would have revealed an unlawful agenda to a Schengen border official, he would then be in a position to challenge your intent even though you have remaining leave. Bear in mind that for people who do not need a visa to enter Schengen, doing so becomes illegal if the the border officials establish intent to violate the rules. For the part of your question about getting a 'less harsh penalty', penalties are levied by national law and are generally not negotiable at the border.

For the second option: In this option you become an overstayer and possibly an illegal entrant. If you get caught, the border officer is entitled to all of the conclusions listed in 'Option 1' (i.e., that your overstay was prompted by personal convenience and therefore avoidable). In this scenario you won't be back in Schengen (or the UK, etc) until there's a change in circumstances.

What this amalgamates to is 'Option 1' is not recommended and 'Option 2' is not recommended. So you can select either option with indifference.

Or you can send for your bf to celebrate Christmas with you in London as an 'Option 3'. Or celebrate an 'early Christmas' in A'dam as 'Option 4'