How to Make It
Place livers in a deep baking dish. Pour milk over livers; cover and chill 8 hours or up to overnight.
Remove livers from milk; discard milk. Rinse livers, and pat dry; arrange in an even layer on a baking sheet lined with paper towels. Sprinkle with 1 teaspoon salt; cover and chill 8 hours or up to overnight.
Heat duck fat and oil in a large skillet over medium-high. Add livers; cook until medium-rare, 1 minute to 1 minute and 30 seconds per side. Transfer livers to a plate. Reduce heat under skillet to medium; add shallots and garlic, and cook, stirring often, until tender and caramelized, about 6 minutes. Stir in Madeira, scraping up any browned bits from bottom of skillet. Cook until liquid is reduced by half, about 3 minutes. Stir in cream and thyme. Bring mixture to a boil over medium-high; stir in livers. Remove from heat; let stand 10 minutes. Remove and discard thyme.
Transfer liver mixture to a food processor. Add lemon zest, ground juniper berries, and pepper. Process mixture, gradually adding butter pieces, until smooth and combined, about 2 minutes. Stir in vincotto and remaining 1 1/2 teaspoons salt. (If desired, pour mixture through a fine wire-mesh strainer to make completely smooth; discard solids.) Store, covered, in refrigerator up to 1 week.