Preheat the oven to 350°F. Season the salmon with the salt, place in a baking dish, and roast until just cooked through, about 18 minutes.
While the salmon is cooking, prepare the sauce. Cut one of the grapefruits into sections by cutting off the top and bottom of the fruit, then standing it on one end and cutting down the skin to remove the woolly white pith and peel. Then, with a paring knife, remove each segment of fruit from its membrane and cut the segments in half. Set the segments aside. Juice the other grapefruit and set the juice aside.
In a medium skillet, heat the oil over medium heat. Add the shallot and cook, stirring, until softened, about 2 minutes. Add the ginger, grapefruit juice, honey, and cayenne and bring to simmer. Cook until the sauce is reduced by about half, about 10 minutes. Add the lemon juice and season with salt. Right before serving, toss the grapefruit pieces and basil into the sauce.
Place the salmon on a serving dish, spoon the sauce over it, and serve.