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Heat 2 Tbsp butter in a 12-inch heavy skillet over medium heat until foam subsides. Add shallot and garlic and cook, stirring occasionally, until softened and golden brown, 3 to 5 minutes.
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Pat livers dry and add to skillet. Cook over medium-high heat, turning once, until browned and just pink inside, about 4 minutes total. Add quatre épices, 1 tsp salt, and 1/2 tsp black pepper and cook, stirring, 30 seconds.
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Add Cognac and tilt skillet over gas burner to ignite (or ignite with a long match; use caution as flames may shoot up high). Cook, shaking skillet gently once or twice, until flames subside.
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Transfer mixture to a food processor and pulse, adding remaining 6 Tbsp butter, 1 Tbsp at a time, until smooth. Transfer to a bowl and chill, surface covered with plastic wrap, until set, about 3 hours. Let stand at room temperature about 15 minutes before serving.