I can't say I see a brown circle. I see a hot spot, a duller inner spill area and somewhat brighter outer spill area. I'm running it on a Eneloop Pro now.
I love the E03H! I just got it 2 weeks after ordering. That is a record for me for delivery from China.
It’s so compact that for a second I thought I was sent the E02 by mistake. I looked up the dimensions and the 78mm E03H is only 6mm taller and has the same 20mm head diameter!
Mine (from AE) came in a cardboard box, not the retail packaging shown in the OP, but that’s fine with me.
It has a premium look and feel, which is not easily conveyed by photos. The surface has a matt, satiny, almost “soft-touch” feel to it. I had to run my fingernail over it to verify there is no rubber coating. Very pleasant.
The first thing I noticed when turning it on is how the wide well-blended beam is the best I’ve seen from a Cree-based flashlight. The hotspot is wide without hard boundaries as it blends nicely into the spill. While it is cold (I wish the Nichia weren’t sold out!), I don’t notice artifacts like corona around the hotspot or distinct color bands.
If held close up against a white surface, the “fried egg” (yellow green hotspot and blue spill) is still present, but at normal viewing distances the light is sufficiently uniform and blended so as not to be distracting. For a cold LED I really like it a lot!
As for the biggest weaknesses I could find, the long-press to turn off takes a bit of getting used to. Also, it is easy for a muggle to just cycle to moonlight and think it is off, or use a single press to turn on in moonlight mode and think the flashlight isn’t working.
Another point is that multi-press commands cause intermediate commands to be acted upon. eg. while in Turbo, double-pressing returns to the normal modes. However, the first press of the double-press will first cycle to Strobe, and upon the second press, it is recognized as a double-press and goes to the normal mode. Similar things happen when pressing four times to get into moonlight engineering mode. I suppose this is a tradeoff between getting instant response from each press versus elegance in UI functions.
One small note is that changes in brightness are handled very pleasantly with a rapid ramping up or down instead of an instant brightness change. It is quick enough not to be annoying, but slow enough to give a satisfying experience.
The headband is simple, and it’s a bit difficult to get the flashlight into it, but it works well enough. Since the EO3H is quite light, I don’t worry about it falling on my face and don’t feel an over-the-head strap is needed.
The diffuser is a nice unique touch and works well for general illumination. Being built-in, there’s a better chance I’ll actually use it. It is a bit difficult to slide up and down, so I wonder if some lubrication will help, or if it will be easier after a break-in period.
Overall, within minutes the E03H has become a favorite. I think it will be my go-to pocketable flashlight when I need some light quickly for a task. Its good mode spacing, regulated output, and good battery life (untested) make it so practical. And perhaps most importantly for satisfaction is that it gives a feeling of joy each time I use it.
I finally got my E03 after having it spend 10 days in US Customs. I don’t see a circle in my beam pattern when wall hunting and am actually pleasantly surprised by the pattern and the tint. Seems like a nice solid light and the only thing I don’t like about it is the switch. Too hard to double click it to get to turbo but I probably won’t use that mode very often.
I threw it into the glove of my car next to my Sofirn SF13 so I’ll probably never use it again 
Does the E03H have reverse polarity protection?
I noticed the manual says: “flashlight won’t work once battery reverse.”
Not sure if that means permanently. 
As curious as I am, I’m not about to try it to find out.
I got one on clearance too. I was interested in the adjustable moonlight. Nice light for that money. I’m pretty tickled with it. Wish I would have bought another one.
I got me a cool white E03H also.
Must say, the 6000K XP-L works very well with the optics.
Yes, thank goodness the moon mode is adjustable (like E02(H)).
Yes! Any idea how to achieve similar results with the Sofirn SP40? And/or the SP33?