Preheat the oven to 400 degrees F.
For the Quail and Stuffing: Spread the brioche cubes on a baking sheet and bake until dry but not browned, 8 to 10 minutes. Meanwhile, heat 2 tablespoons of the olive oil in a medium skillet over medium-high heat. Add the chorizo and cook until crispy, about 3 minutes. Add the celery, garlic, onion, sage and apricots and cook, stirring occasionally, until tender, about 8 minutes. Transfer to a large bowl and cool slightly.
Add the brioche cubes to the vegetables and toss. Add the egg, salt, pepper, and enough of the chicken broth to moisten the bread, and toss.
Season the quail inside and out with salt and pepper. Stuff each quail loosely with the brioche mixture and tie the legs together with kitchen twine. Put the remaining stuffing into a lightly buttered casserole dish. (The recipe may be prepared up to this point 1 day ahead, covered, and refrigerated.)
Bake the stuffing until browned on top, about 30 minutes. Meanwhile, heat 1 tablespoon of the remaining olive oil in an ovenproof medium skillet over high heat. Add half the quail and cook, turning as each side gets a rich mahogany brown, about 8 minutes in all. Transfer to a low roasting pan or casserole dish just large enough to hold the quail. Repeat with the remaining quail, adding more olive oil if necessary. Reserve the skillet and drippings. Transfer the quail to the oven and roast until an instant-read thermometer inserted in the cavity reads 160 degrees, about 20 minutes.
For the Sauce: Add the shallots to the reserved drippings in the skillet over medium heat and cook until tender, about 5 minutes. Add the red wine and simmer until reduced by about half, stirring occasionally with a wooden spoon to scrape up the browned bits. Add the demi-glace or chicken stock, the apricots and currants. Simmer until fruit is tender, 8 to 10 minutes. Remove from the heat and keep warm.
Transfer the quail to a plate and tent loosely with foil. Whisk the butter into the sauce a bit at a time until the sauce is glossy and coats the back of a spoon. (If necessary, gently reheat the sauce before whisking in the butter off the heat.)
To serve, spoon some of the stuffing into the centers of 4 dinner plates. Set 2 quail on top, spoon some sauce over, and ring with some of the Wilted Greens.
Heat the olive oil in a large skillet over medium-high heat. Add the shallots and chard stems and cook, stirring occasionally, until brown, about 6 minutes. Stir in the chard leaves and cook, tossing, until wilted, about 2 minutes. Season with salt and pepper.
Brown chicken stock adds depth and flavor to this simple pan sauce. It is easy to make and great to have on hand in the freezer. Visit foodnetwork.com to find a recipe (search for "brown chicken stock").
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