Yup, this sounds very familiar.  My mother enjoys this, but hasn't had it since my grandmother passed away.  "Pul la gel" is a congealed aspic dish with meaty leg or ankle bones, garlic, parsley and perhaps eggplant, etc., loaded with garlic.  It's served cold and whenever I saw it on the table, I ran like hell.  I would check Armenian recipes for a vegetarian version.  It sounds like it could be a sauteed eggplant dish, the way you describe it...fry up some onions in good olive oil until slightly charred (add a tsp of sugar to the fry), add some chopped garlic to taste, don't burn it--so lower the heat, then add some chopped peppers and chopped fresh parsley to the mix and some shredded eggplant (use a cheese grater or your food processor).  When all is nice and soft, add salt and pepper to taste and refrigerate.  Don't overdo the salt when it's hot, cold it will taste more salty.  Correct the seasonings when it's cold and serve drizzled with olive oil and a squeeze of lemon.  I would give you exact proportions, but I cook the old fashioned way!