UKC

I'm casually looking for places to stay (two families) in the Alps in the summer. Ideally whole villa with four bedrooms.

What I'm finding is when using Booking.com or AirBnb there's loads of places on the French sides (around Chamonix) and at lower cost than on the Italian Side around Courmayeur.

The fact that accommodation is more plentiful and cheaper on the French side leads to me think that Italian venues choose to advertise in a different way.

Does anybody know where I can find them?

From memory in the dolomites trying the local tourism website will produce more results.

There's some problems with Airbnb ( and others) in Italy though they just agreed to pay $620m in back tax, the adjustments in the flat-rate tax regime for short term rental seem to have made things "interesting".

Courmayeur and Northern Italy generally is short on budget accommodation, with the exception of camping. I'm not surprised by what you've found.

Maybe try German booking websites - Casamundo? Italy probably gets more tourists from Germany than elsewhere.

https://www.courmayeurmontblanc.it/en/stagioni/summer/

Local tourist sites are often best in many parts of the European mainland.  Run by local government administrators they can be a little clunky and the process flow from looking to booking can be odd, but you should find more stuff including local apartments attached to farmhouses etc where the owner speaks no English and have never heard of ABnB and booking.com (The tourist people will help with communication as will Google translate - make sure you download the language file on the app for the area). 

You may need to pay deposits and final amounts through a direct bank transfer.  You may need to get the IBAN number for the bank account and the bank name and address and the account owners name and address - again its a faff but I have never had any issues.  Running emails through google translate works well.

Try browsing this...it's quite popular: https://www.roterhahn.it/en/farm-holidays/indulgence-on-the-farm/half-board

It's only Italian South Tyrol & no idea what prices are like mind.