What part of oatmeal cookies are making them soft / chewy?
There are several ingredients and procedures that work together to determine the structure and texture of a cookie.  At the end of this recipe on ChefSteps, there is a very detailed explanation.  I am sure it is possible to make a savory version, you are just going to have to be creative in your approach.  If you search their site, they also have tips for making gluten free cookies more "cookie-like."  You might explore the use of different sugars, which have differing levels of sweetness.  You can shop Modernist Pantry, for example, as an online source of these ingredients.  

In direct response to your question, and according to the information in the link I provided, the following ingredients contribute to the texture of a cookie: sugars, butter (its temperature...and how they are mixed), liquid-to-flour ratio, temperature of the dough when it is baked, and whether or not you choose to compact them after baking...so, there are a lot of variables that you will need to experiment with.

Alternately, for savory applications, you could use a tuille.