How is this cutting board handle possible? The only way I can think of is that it was done by hand with a gouge, but it looks too clean for that. Can an inset handle, such as the one pictured below, be done with power tools?
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Two ways spring to mind immediately.
One way would be with a router, a core box bit, and a jig.
The jig would clamp onto the end of the cutting board and provide a surface for the router to ride on. This would give you a true reproduction of the effect in the photo above. (In my drawing, the curve is exaggerated for effect.) Mount two blocks on your router base to make sure it can't move side to side, and have at it.
A second way would be to just have a plunge router and a core box bit.
Set up a jig to make a platform large enough for the router to ride on, then start at one end, plunge, move to the other end, and lift.
Although you could find a way to form that handle with a router, I'd guess that whoever made that board used a shaper with a cutter like this: