Hey, Orps!
I think your doe would be considered a Vienna Carrier (VC) since, having produced BEW offspring, she must have the Vienna gene even though you can't see it expressed in her. VC's are not exactly rare, but they are pretty unusual. They do have an advantage over the VM's, in that they are showable.
Seriously, though, there really isn't a "brown-eyed gene." There's the Vienna gene (V), and the non-Vienna gene (v). As you know, a rabbit that has two copies of the Vienna gene is a white rabbit with blue eyes, and a rabbit that has two copies of the non-Vienna gene can be any other color
except BEW. It's those rabbits that have one Vienna gene, and one non-Vienna gene (Vv), that get so confusing. The vast majority wind up looking something like Dutch rabbits, with white feet, a blaze on their faces, maybe even a white belt across their shoulders. Some, though, have much less white, maybe just a couple of white toes or a white snip on the nose. They may have blue eyes, brown eyes, or even one of each. And then there are the VC's, that show no signs of the Vienna gene at all, though they obviously have it. I have seen a few different explanations of how the gene can only affect some, but not all, of the rabbit's coat like it does, but that gets pretty technical. As to why one rabbit should wind up with a lot of white, and another with very little white or none at all - my best guess is that there may be modifiers that affect how the gene gets expressed, just as there are with other patterns. The modifiers may not even be genes.