Rinse rice in several changes of cold water in a large bowl until water runs clear. Drain in a colander. Place rice in a 4-quart heavy saucepan, then add water (amount according to the instructions on the package) and bring to a boil.
Reduce heat to low and cook, covered, again according to the package instructions, usually 15-20 minutes.
Remove from heat and let stand, covered and undisturbed, 5 minutes. Fluff rice with a fork and let cool to almost room temperature.
Chill, covered with plastic wrap, at least 4 hours.
Heat a large (12-inch or more) heavy skillet over medium-high heat. Add 1 Tbsp of the oil to coat the bottom of the pan.
When oil just begins to smoke, stir-fry ginger, white and pale green parts of scallions, and salt until fragrant, about 1 minute. Add the remaining 2 Tbsp oil to the pan.
Crumble rice into the pan and stir-fry until lightly browned, 10 to 12 minutes. Remove from heat, then add scallion greens, pineapple, and sesame oil, tossing to combine. Season with salt.