Aman in Montenegro

There are some places like this in Puglia also- however typically they are part of a "touristic village" as it is called- something like a very high end Club Med. Again the Virtuoso team should be able to sort this out.

I don't know if you consider Turkey part of Europe, however if you do the new Aman there looks absolutely stunning and should meet the conditions I think (I have not been there- just seen reviews).

I imagine there must be something like you describe in Formentera- however I don't know for sure- I rented a little villa with a pool there for a week one summer and had a cook at night- it was good. Heaps of places for rent at the moment.

The Marbella Club in Spain has some private beachfront villas- unfortunately when I went there I received dreadful service and won't return- the location is quite nice however.