Step 1For the sauce, saute the ginger, 2 tablespoons of the shallots and 2 tablespoons of the scallions in 1 tablespoon of canola oil over medium-high heat until they turn a rich brown, about 3 minutes. Add the brown sugar and cook until caramelized, about 1 minute. Add the wine and reduce until the wine is only about 2 tablespoons, about 20 minutes. Add the veal stock and reduce to 1 cup liquid, about 45 minutes. Season with one-quarter teaspoon salt and one-eighth teaspoon pepper.
Step 2Butterfly the quail by using scissors to cut through the cavity down one side of the backbone of the birds. Place the quail on a cutting board and gently press down with the heel of your hand to flatten them slightly. Pat dry. Season the quail with salt and pepper.
Step 3Mix together the remaining scallions, parsley and remaining shallots and stuff the mixture into the cavities of the quail. Press the sides together to hold in the herbs.
Step 4Heat a cast-iron skillet over high heat until hot. Add the remaining canola oil and heat until smoking. Place the quail in the pan, front-side down. Add the butter and cook until caramelized, about 2 minutes.
Step 5Flip the quail and caramelize the other side. Cook until just heated through, about 3 minutes.
Step 6Remove and pat dry with paper towels. Cut each quail in half. Arrange 4 halves on each plate. Spoon about a quarter cup of sauce around the quail.