Remove duck livers from refrigerator 20 minutes before cooking to bring to room temperature. Pat dry with paper towels and trim any connective tissue or green spots.

Heat 2 tablespoons butter in a large skillet over medium heat. Add sliced onions with a pinch of salt and cook slowly for 15-18 minutes, stirring occasionally, until deeply golden and caramelized. Set aside to cool.

In the same skillet, add 2 tablespoons butter and heat over medium-high. Add minced garlic and cook for 30 seconds until fragrant.

Add duck livers, thyme, salt, black pepper, and nutmeg. Cook for 5-6 minutes, turning occasionally, until livers are browned outside but still slightly pink inside (internal temperature 145°F).

Remove from heat and add cognac, stirring to deglaze the pan. Allow to cool for 10 minutes.

Transfer liver mixture and half the caramelized onions to a food processor. Add remaining softened butter and heavy cream. Process for 2-3 minutes until completely smooth and silky.

Taste and adjust seasoning if needed. Pass through a fine-mesh sieve for extra-smooth texture (optional).

Transfer pâté to ramekins or a terrine mold. Top with remaining caramelized onions, arranging decoratively.

Cover tightly with plastic wrap pressed directly onto surface and refrigerate for at least 4 hours or overnight.

Before serving, let stand at room temperature for 15 minutes. Garnish with fresh thyme and serve with toasted bread slices.