Heat the butter in a heavy 3-quart (3-L) saucepan. Add the onion and fresh ginger and saute over medium heat until the onion is translucent but not brown.
Add the rice and cook, stirring, until it begins to whiten. Stir in the wine and allow the mixture to simmer until most of the wine has evaporated.
Place the saffron in a small dish and pour 1 cup (250 ml) of the hot stock over it. Set aside for a few minutes.
Have the rest of the stock simmering in a separate saucepan.
After the wine has evaporated, stir in the 1/2 cup (125 ml) of the vegetable stock and continue to cook the rice mixture, stirring, until most of the liquid has been absorbed.
Keep the mixture at a steady simmer.
Stir in the cup of stock with the saffron and stir until most of the liquid has evaporated.
Continue adding stock, a couple of ladles at a time, stirring and adding more as the stock is absorbed by the rice.
Regulate the heat so the rice and stock cook at a steady simmer.
After about 15 minutes, the rice should have swelled and become somewhat tender, but still a bit hard in the middle. There should still be some stock left at this point.
Add the scallops. Stir, then continue adding stock for another few minutes, as needed, until the rice is plump, offers only the slightest resistance to the bite, and there is just enough thickened, creamy, sauce-like broth to moisten the rice.
Season with salt and pepper and serve at once.