what's the best way to quilt on buttercream?
I agree a mat or similar is best.
If your b;cream is not crusting, put a piece of tulle on the icing 1st, then the mat.
I have used a piece of plastic covering ceiling lights instead of getting an actual mat. This was way back before the mats were common I didn't even have to buy it. At Home Depot they were throwing out a broken one & just gave it to me.