How to Make It
Place chicken livers in a bowl, and add the buttermilk and Tabasco. Refrigerate 8 hours or overnight.
Drain the livers; place them on a clean paper towel, and pat dry. Season with 1/2 teaspoon salt.
Melt the clarified butter in a large pan over medium-high. Add the livers, and sear until golden brown, about 1 minute per side. Transfer to a plate. Add shallot, thyme, and bay leaf; cook, stirring often, until shallots are translucent. Add the apple brandy and lemon zest, and cook until almost the pan is almost dry, about 2 minutes.
Remove and discard thyme sprigs and bay leaf. Add livers, shallot mixture, 1/2 cup cold butter, and remaining 1/2 teaspoon salt to the bowl of a food processor or blender. With processor running, slowly add the heavy cream. Once the mixture is smooth, pour contents through a fine wire-mesh strainer into a bowl, pushing on solids with a plastic dough scraper. Discard any solids. Pour the mousse evenly into 6 jars, filling each about two-thirds full. Gently tap jars on the work surface to flatten the mousse.
Wipe pan clean; add remaining 1/4 cup cold butter, and cook over medium until melted and browned, about 6 minutes. Remove from heat, and let cool slightly. Spoon enough melted brown butter into each jar to cover the mousse, and chill in the refrigerator until set, about 4 hours. Serve with pimiento cheese, deviled eggs, muscadine jam, pickles, cornichons, and grilled bread.