Put the water into a straight sided skillet or pot with a lid. Add 3 of the lime halves (squeezing the juice into the water before adding), 5 tablespoons of the honey, the ginger, salt and peppercorns and bring to a boil over medium-high heat. Reduce the heat to a simmer, cover, and cook for 10 minutes to infuse the water with flavors. Remove and reserve 1/2 cup of this poaching liquid. Remove the pot from heat and add the tea. Allow the tea to steep for 3 to 5 minutes. Carefully slide the salmon into the water. Cover and poach until the fish is just cooked through and firm to the touch, about 6 to 7 minutes.
Meanwhile, in a small pot over low heat, simmer the reserved 1/2 cup of liquid along with the juice and zest of the remaining lime half, and remaining 1 tablespoon of honey. Cook until the liquid is reduced by 2/3 and thickened, 7 to 10 minutes.
Remove the fish with a slotted spoon and arrange on serving plates. Drizzle a little bit of the sauce over each piece salmon before serving.
This recipe has been updated and may differ from what was originally published or broadcast.