Lay the fish fillets skinned side up on a cutting board. Slice each fillet in half lengthwise to make 12 strips. In a small bowl mix the ginger, 1/4 tsp. salt, and 1/4 tsp. pepper. Sprinkle the spice mixture evenly over all the fish and then sprinkle with 2 Tbs. of the chopped mint. Roll each strip into a coil, starting with the fatter end and aligning the roll along the cut edge. Secure with a toothpick, pushing it into the thin end and through the other side.
Sprinkle the shallots over the bottom of a 10-inch straight-sided sauté pan. Arrange the fish coils cut edge down in the pan. Pour in the wine and 1/3 cup water. Turn the heat to medium high and bring the liquid to a simmer. Adjust the heat to maintain a gentle simmer, cover, and poach the fish until cooked through, 4 to 8 minutes. Use a slotted spoon to transfer the fish to a warm plate. Tent with foil while finishing the sauce.
Increase the heat to high and boil the liquid until it’s reduced to about 3 Tbs. (It should just barely cover the bottom of the pan.) Add the cream and boil for 30 seconds. Reduce the heat to low and whisk in 2 slices of the cold butter, the remaining 1-1/2 Tbs. mint, and the chives. When the butter is almost melted, add another slice and whisk until mostly melted. Repeat with the remaining butter, 1 slice at a time. (Take care not to overheat the sauce or it will separate.) Season to taste with salt and pepper.
Remove the toothpicks from each piece of fish. Serve the fish (3 pieces per serving) drizzled with the sauce.