What can I do to make my eyebrows grow back after they've been gone for around a year? (Photo)

I recommend getting a formal evaluation with a hair loss expert. Prp and progesterone can be used to regrow eyebrows. Best, Dr. Emer

It's not common to lose eyebrows form atopic dermatitis. However, another issue with an immune base could be present. Please see a dermatologist for an up close examination and to confirm the diagnosis.  Steroid injections are likely the best option for success at this point. 

First obtain a reasonably definitive diagnosis. If autoimmune issues are involved see an endocrinologist or alternatively a Integrative Medicine or Functional medicine provider. My experience has been the latter two types of providers are more likely to be more proactive with addressing the root cause and issues.
Once the root cause is addressed, you might try PRP hair regeneration.
I wish you success in finding a resolution to your problem.
Warmly,
Arbella Sarkis, MD

Was there any specific cause, as if this happened for no known reason then you should request some tests to be carried out to understand the true cause of the hair loss, probably best to initially speak to your Doctor and ask for a referral to see a Dermatologist. Once the cause is known and understood, then and only then you can look at a resolution.
An option could be a Transplant of some kind but at this stage it would be unwise to proceed down this route until proper tests have been carried out and results of the cause of the hair loss are noted.

It is difficult to say if eyebrow transplants would be effective for you. There is a link between atopic dermatitis and alopecia areata. If you in fact have areata thebgrafts may not take. If this is simply atopic dermatitis then there’s a better chance that as long as the condition is well maintained that thevgrafts will take. I would recommend setting up a consultation with a provider well-versed in hair loss so that you can discuss your options. 

if you have lost your eyebrow hair from an autoimmune disease if you do hair transplant there is no guarantee that Hair transplanted hair will stay. you need to check with your dermatologist. Sometimes steroid injection may help or you can do microblading or tatoo. 

First I would really want to make a diagnosis as to why your eyebrows disappeared. Once I knew the answer, if you don't have some autoimmune disease that caused it, a hair transplant is a good option.