In a medium-sized skillet over medium heat, melt the butter.
Add the ginger, garlic and onions, stir frequently until the onions are transparent. Add the rice, turning frequently until well coated. Add the coconut milk, water, salt and pepper and bring to a boil. Reduce the heat to low, cover and simmer for approximately 20 minutes (until the liquid is absorbed.)
Remove from heat and let stand 5 to 6 minutes. Spoon the rice into a serving bowl, add the basil pesto and toss with fork to fluff and distribute the flavor.
Notes
For Sushi Ginger- ask at your market's sushi counter. They should be able to give you some. And sometimes they even have little containers of them (or jars) for sale too.