Melt 3 tablespoons butter in a large skillet over medium-high heat. Add livers, mushrooms, scallions, garlic, and paprika. Cook, stirring occasionally, until livers are cooked through, about 5 minutes. Stir in 1 teaspoon salt. Add wine and thyme. Reduce heat to low; cover. Cook until mushrooms are very soft, about 10 minutes. Let mixture cool completely.
Process mixture and remaining 12 tablespoons butter in a food processor until smooth. Stir in 1 1/2 teaspoons salt. Transfer pate to an airtight container or a ramekin; cover with plastic wrap directly on surface. Refrigerate until firm, at least 2 hours or overnight. Serve with bread and sauteed apples.