Yes, a crooked knife or a hoof knife helps a lot for scooping out concave surfaces.

Another alternative is to use wood tongs to hold a live ember to the business side of the spoon and burn a hollow into it.

A third is to make lots of crosshatch cuts, very close together, in the area to be hollowed out. Then scrape that material away from the stick. Like the ember, it’s crude but it will get the job done.