Trim the livers of any excess fat and tough connective tissue. Dry them very well and set aside on a layer of paper towels.
In a large skillet over medium heat, melt the duck fat (or 2 tablespoons of butter). Add the liver in a single layer (do two batches if necessary) and cook until they are beginning to brown (3-4 minutes). Turn them and cook until the livers are just barely pink inside (2-3 minutes), Don't cook them too long or they'll be dry. Remove them to the bowl of a food processor.
Add the onions and thyme and cook over medium heat, stirring occasionally, until onions are very soft and lightly brown at the edges (7-10 minutes).
Remove the pan from the heat, and pour the brandy into the skillet. Put back on the heat and simmer, scraping up any browned bits from the bottom of the pan. Reduce the liquid for about a minute then pour over the liver mixture. Add the salt. Process until mixture is very smooth, scraping down the sides of the bowl as needed.
With the processor running, add softened butter one tablespoon at a time until the mixture is very smooth and creamy. It may seem loose but it will stiffen up a lot in the fridge. Add pepper and any additional salt, to taste*. Pack into small jars or ramekins and smooth tops with a spatula or knife. When it's cool enough, cover with plastic wrap, pressing the film directly against the surface of the pâté.
For longer storage, pour enough clarified butter to cover the top of each ramekin and add a decorative thyme sprig. Chill until the butter is firm and cover with plastic wrap or a lid.