Preheat the oven to 450 degrees F.
For the citrus vinaigrette: In a small saucepot, combine the ginger, shallots, blood orange juice and navel orange juice. Bring to a boil over high heat and reduce the juice by about half until it starts to have a thick consistency. Reduce the heat to a low simmer and slowly drizzle in the extra-virgin olive oil while whisking, creating an emulsion. Season with salt and pepper. Set aside.
For the green papaya salad: Cut the green papaya into manageable, stable pieces and then thinly slice into julienne. Add to a bowl and combine with the fish sauce, extra-virgin olive oil, cilantro, lime juice, carrots, onions and some salt and pepper. Mix everything together and set aside.
For the fish: Divide the oil between 2 ovenproof saute pans and set over medium-high heat until the oil is very hot but not smoking. Season the striped bass on both sides with salt and pepper. Place the bass in the pans (2 in each) presentation-side down and sear until golden brown. Turn the fish over and put the pans in the oven until a metal skewer can be easily inserted into the fish and feels warm to the touch when left in for 5 seconds, 2 to 3 minutes. (If the striped bass is only 1 inch or thinner, the fish can be cooked all the way on the stove top, without going into the oven.)
While the striped bass is cooking, reheat the citrus vinaigrette, whisking over low heat.
To serve, arrange a bit of the green papaya salad in a nice pile in the center of 4 plates. Place the striped bass on the piles and put a little more of the salad on top of each piece of fish. Spoon the citrus vinaigrette around the fish and serve immediately.
When choosing the fish fillets for this dish, try to get uniform fillets cut from the head end of the fish. These fillets will be about 1 1/2 to 2 inches thick. If you can only find thinner tail fillets, you will need to cut the cooking time a bit or simply cook the fish completely on the stove rather than finishing it off in the oven.