Yes, I've made a bunch of small bowl adzes over the years. And that "eye" is the hard part.
The ones I made I used something of a "shortcut" in making. I made them from an old Claw Hammer - the old style ones that take a tapered square wooden handle.
I cut off the "claws", and then forged the hammer face side into the shape and size of bowl adze that I wanted. I also took extra care not to distort that eye in any way. Just be sure to forge the hammer portion up flush with the top of the eye as you are drawing it out. Then you can gently curve the whole top to match the swing you will be using when chopping with the adze. And you can then cut off the extra wood handle to also be flush with the top.
The advantage of starting with an old hammer head is that you already have that "eye" fully formed up. It's already rectangular in shape and slightly tapering. And the steel is excellent for an adze. They make into great bowl adzes.
Otherwise you have to start with large enough steel, and then punch/drift a whole lot to get that eye large enough and "deep" enough to work well with your wood handle. Or you have to wrap the bar around and weld it - like making a tomahawk.
I have made two this last year by punching/drifting out the eye, but it was HARD WORK. I did it for the experience, and also for the "look" of the finished head. But I also knew I would never be able to get anywhere near the right "compensation" from selling them that I had put into making them. The only way to make them is for your own personal satisfaction.
Historical note: There are a number of original tomahawks that were turned into adzes or garden hoes by a local blacksmith. You have to heat up the head, and then twist the blade 45 degrees and "curve" it a bit. And then re-heat-treat. They do work well, but tend to be kind of rare. Two were found down at Fort Quieotnon (sp) in the Ohio/Illinois territories, and several journal entries about having the local smith convert some up at Fort Robert in the Canadian territoris.
Mikey - yee ol' grumpy German blacksmith out in the Hinterlands
p.s. A number of people have taken ballpeen hammer heads and forged them up into spike hawks. They do work pretty well. And there are several original spike hawks in the books/museums that have all the look/shape as if they were made the same way.