Halve 1 lime and squeeze the juice into a large straight sided skillet or pot with a lid. Add 6 cups water, the squeezed lime halves, ginger, and peppercorns and bring to a boil over medium-high heat. Reduce heat to a simmer, cover, and cook for 10 minutes to infuse the water with flavor; reduce heat to lowest setting, carefully slide salmon into the water, cover, and poach until fish is just cooked through, 5 to 7 minutes. Remove the fish with a slotted spoon and cool completely before transferring to an airtight container. Add about 1/2 cup poaching liquid to the container to keep the fish moist and chill in the refrigerator until ready to serve.
Meanwhile, zest the remaining lime and add about 1/2 teaspoon zest to the bowl of a food processor; add the juice from half the lime to the bowl (should be about 1 teaspoon juice). Add the basil leaves, a pinch of salt and a few grinds black pepper and pulse until it begins to turn into a paste. Add the creme fraiche and puree until very smooth. Transfer to a serving bowl and refrigerate until ready to serve.
To serve, plate the cold salmon with a drizzle of lime basil cream over the top.