Sauté onions and ginger: Heat a large sauté pan on medium high heat. Swirl in a tablespoon of oil to coat the pan.
When the oil is shimmering hot, add the ginger and the white and pale greens parts of the green onions.
Stir fry green onions and ginger
Sprinkle with salt and stir fry until fragrant, about a minute.
Brown the rice: Add the remaining 2 tablespoons of oil to the pan. When the oil is hot, add the cooked, leftover rice to the pan, breaking it up with your fingers as you sprinkle it into the pan.
Let the rice fry in the pan without moving it for a minute or two, until it starts to brown. Then stir it so that it turns over in the pan, and let it cook for a minute or two more.
Stir in pineapple, more green onions, soy sauce, sesame oil: Remove the pan from the heat and stir in the chopped pineapple, sliced green onion greens, soy sauce, and sesame oil.
Add salt to taste and serve.