Reduce heat to medium and add another tablespoon butter to skillet. Add shallots and season with salt and pepper; cook, stirring, until translucent, about 5 minutes. Add pears, thyme, cloves, cinnamon sticks, brown sugar, and 1/4 cup water. Cover and cook, stirring occasionally and adding water as necessary to prevent burning, until pears are soft and easily pierced with the tip of a sharp knife, about 15 minutes.

Remove skillet from heat; uncover and add brandy, scraping up browned bits at bottom of skillet to deglaze. Remove thyme and cinnamon sticks from skillet and discard.

Cut remaining 5 tablespoons butter into small cubes. Transfer remaining contents of skillet to the bowl of a food processor along with chicken livers, cream, vinegar, nutmeg, and cut butter. Process until mixture is very smooth; season with salt and pepper.