Freeze milk in a shallow dish, scraping once or twice with a fork to break up crystals, until frozen, about 1 hour.
Pull skin with fat off duck breast with your fingers, using a knife when necessary, then cut both skin with fat and breast meat lengthwise into 1-inch pieces that will fit in grinder. Chill meat and skin with fat, wrapped separately in plastic wrap, in freezer until firm but not frozen, about 1 hour.
Set a medium bowl in a larger bowl of ice and cold water under grinder to catch ground meat, then feed meat (only) through grinder. Replace medium bowl in ice with a large metal bowl and feed meat through grinder a second time, adding spoonfuls of frozen milk as you go. Chill, covered with plastic wrap, in refrigerator.
Feed duck skin with fat through grinder twice into a bowl set in a larger bowl of ice and cold water, then add to ground duck meat and set bowl in larger bowl of ice.
Add remaining duck terrine ingredients to ground-duck mixture and mix with your hands or a wooden spoon until combined well. Chill, covered with plastic wrap, in refrigerator at least 8 hours to marinate meats.
Bring wine, vinegar, sugar, salt, thyme, and bay leaf to a boil in a 1- to 1 1/2-quart heavy saucepan, stirring until sugar is dissolved, then add whole shallots and cover surface of liquid with a round of parchment or wax paper. Simmer shallots vigorously until tender, about 40 minutes, then transfer from cooking liquid to a bowl with a slotted spoon and discard thyme sprig and bay leaf. If liquid isn't syrupy, boil until reduced to about 1/3 cup.
Pour over shallots and cool.
Put oven rack in middle position and preheat oven to 325F.
Line bottom and all sides of terrine with fatback (or caul fat), overlapping edges slightly and leaving a 2-inch overhang on long sides. Rub some of duck mixture onto fatback lining to help the rest adhere, then pack in about two thirds of remaining duck. Create a wide trough lengthwise along the middle with back of a spoon. Embed drained shallots, reserving Port syrup, pointed ends down in trough. Pack remaining duck mixture on top. Fold overhang (adding more fatback if necessary) to cover top completely, then cover terrine with a double layer of foil. Rap mold firmly on counter to compact terrine.
Bake terrine in a water bath until thermometer inserted diagonally through foil at least 2 inches into center of meat registers 155 to 160F, 13/4 to 2 hours.
Remove foil and cool terrine in mold on a rack, 30 minutes.
Put terrine in mold in a cleaned baking pan. Put a piece of parchment or wax paper over top of terrine, then place on top of parchment another same-size terrine mold or a piece of wood or heavy cardboard cut to fit inside mold and wrapped in foil. Put 2 to 3 (1-pound) cans on terrine or on wood or cardboard to weight terrine. Chill terrine in pan with weights until completely cold, at least 4 hours. Continue to chill terrine, with or without weights, at least 24 hours to allow flavors to develop.
Run a knife around inside edge of terrine and let stand in mold in a pan with 1 inch of hot water (to loosen bottom) 2 minutes. Tip terrine mold (holding terrine) to drain off excess liquid, then invert a cutting board over terrine, reinvert terrine onto cutting board, and gently wipe outside of terrine (fatback) with a paper towel.
Let terrine stand at room temperature for 30 minutes before serving, then cut into 1/2-inch-thick slices and serve on plates drizzled with reserved wine syrup.
*Available at dartagnan.com.
Cooks' notes:Terrine can be marinated (before baking) up to 24 hours. Shallots can be glazed 1 day ahead and cooled, uncovered, then chilled in cooking liquid, covered. Terrine keeps, wrapped in plastic wrap and chilled, 1 week.
