Hotel search engine that allows to search for rooms with a desk?

I think your best bets would be:

• AirBnB (you can search for a place with a place for a laptop, and that means a desk)
• Searching on Booking.com for apartments instead of plain rooms. The cost is the same, more often than not.

Small notes:

1. After all my traveling in Europe I've yet to find an hotel which has not a desk

2. I suggested Booking.com because it is the one I know best. Obviously the same search criteria, when present, is valid for other search engines.

I'm not aware of any hotel search engines that allow you to search for a desk, or filter on a desk.

However, in my experience most hotel rooms have a desk. (at least in well known brands) I usually stay in hotels from known brands (Marriott, Hilton, Best Western, Choice hotels, Radisson, ...) and have yet to encounter a room without a desk. I have read that Marriott is redesigning some rooms and these would no longer come with a desk, still these are currently rather exceptions.

My strategy would be to search for hotels that fit your other criteria and then contact the hotel to make sure the rooms come with a desk. It would allow you to ask some other details about the desk (ergonomy, ...?) and you could also have the reception make an additional note on your reservation that you absolutely need a well-sized desk as you will be using it multiple hours/day.

I think this strategy gives better guarantees to a proper desk than just relying on search-engines.