How to Make It
Rinse rice in a fine wire-mesh strainer under cold running water, agitating with your hands, until water runs clear, about 3 minutes. Let rice drain in strainer 30 minutes.
Meanwhile, fold an 8-inch square piece of cheesecloth into quarters to make a 4-layer, 4-inch square. Grate ginger on medium holes of a box grater over the center of the cheesecloth square. Gather edges of cheesecloth, and squeeze ginger over a small bowl to equal 1 tablespoon ginger juice. Discard solids; set ginger juice aside.
Place drained rice, master dashi, carrot, and soy sauce in a small heavy-bottomed saucepan. Bring to a boil over high. Reduce heat to low; cover and simmer 10 minutes. Remove from heat; let stand, covered, until rice is cooked through, about 10 minutes.
Transfer cooked rice to a bowl; fluff with a fork, and stir in ginger juice. Serve warm or at room temperature.