In a large frying pan, melt 2 T of the butter over moderately low heat. Add onions and cook until onion i ssoft, about 5 minutes. Add garlic and cook for 1 minute longer. Transfer to a food processor or blender.
Melt remaining 4 T of butter in the same pan. Add livers and saute over medium-high heat, tossing, until browned outside but still rosy inside, 3 to 5 mintues. Sprinkle withk salt, thyme, tarragon, pepper, and Cognac. Cook, scraping up any browned bits from the bottom of the pan, for 1 minute.
Scrap liver and pan juices into food processor. Puree until smooth. Scrape into a serving bowl or crock. Let cool to room temperater. Cover and refrigerate until cool, several hours or overnight.