Can a US pilot residing in the EU fly N-reg under IFR on a US PPL?
Long story short, European residents apparently require an EASA license to operate a foreign aircraft, even if they also hold a foreign license from the country the aircraft is registered in.

European regulations are really difficult to pin down because implementation is delegated to member states, however it looks like as a resident in an EASA country you do need an EASA license to operate an N-registered aircraft based there. There are many online sources that say that, although they typically don't link to actual regulations. Several of them mention that you get a 12-month period to acquire the EASA license, during which you can still fly with your foreign license.
For example:
AOPA blog article:

The European Aviation Safety Agency, a pan-European regulator, had
passed a regulation some years earlier requiring that European
residents acquire a European equivalent license to fly an N-registered
aircraft in Europe. This requirement didn’t apply to nonresident
foreigners.

A UK Flight Examiner's website:

If your N-reg aircraft would be classified as an EASA aircraft if you
registered it under the G registration, AND it is based in the UK now,
you do need either an EASA licence to fly it or an EASA validation. If
you wanted to fly it outside the UK, you would need your FAA licences
too.

The underlying EASA regulation appears to be REGULATION (EC) No 216/2008, which says that it applies to foreign aircraft if the operator is based in Europe (Article 4, paragraph 1(c), emphasis mine):

registered in a third country and used by an operator for which any
Member State ensures oversight of operations or used into, within or
out of the Community by an operator established or residing in the
Community

Paragraph 2 says that the regulations apply to personnel too, it's not just about the aircraft itself:

[...] Personnel involved in the operations of aircraft referred to in
paragraph 1(b), (c) or (d) shall comply with this Regulation

The tricky part is that EASA leaves it to each member state to actually implement the regulations and sometimes they implement at different times (see comments in the AOPA article above). I couldn't find the Dutch regulations, but the UK regulations do confirm that only non-residents are exempt from European licensing requirements. Air Navigation Order, Article 149, emphasis mine:

This paragraph applies if the operator of the aircraft is neither
resident nor established in the European Union, and the person
acting as a member of the flight crew is the holder of an appropriate
licence granted or rendered valid under the law of the country in
which the aircraft is registered or the State of the operator.

(As an aside, the ANO article is written in a very confusing, double-negative construction, but it does line up with other sources.)
Because EASA delegates to each member state, the best way to get a definitive answer that applies to your situation is to contact the Dutch civil aviation authorities. When and if you do find out what the requirements are, it would be great if you would come back here and add your own answer to this question. There's surprisingly little definitive, sourced information available about this and a first-hand answer would be really helpful.