I had this in Bangkok, specifically at Don Pino Italian restaurant from Srinakarin district.
The sauce tasted like basil pesto, you can even see small pieces of blended basil in the sauce. It was wrapping gnocchis in a non-clingy way (I don’t think there was cheese, or at least I couldn’t smell or identify it).
The taste was balanced/light basil pesto. The texture was “silky”, didn’t feel light heavy cream or too creamy at all.
I would like to try to recreate this at home, any idea?
Some variant on "make no-cheese pesto, but thin" sounds right from your description. Up to you if you want to or feel the need to use pine nuts as part of that (I've largely dropped them as now too absurdly expensive for my taste - sunflower seeds get 99% of the effect at something like 10% of the price - it's mostly basil and lemon for the flavor when I make it.)
Note that I make no-cheese pesto a lot, (it freezes better than cheese pesto) and a sauce quite like this, so far never. I'd be frustrated by the waste of good basil that didn't stick to the food, or the need to mop it up with bread.
So, throw some garlic and lemon juice in a food processor or blender, add nuts and basil and oil, then dilute with more oil or water or lemon juice to taste (either to match what you had, or to suit yourself, as you like.)
Speculating perhaps an egg yolk, some lemon juice or vinegar, and the oil (added s-l-o-w-l-y) in the machine first to make mayonnaise as a base, so your oils and water-based liquids are emulsified well. Thin down to the right consistency, of course. That might be part of the "silky" texture.