Discard the giblets from the hens or reserve for another use. Using kitchen shears, cut along both sides of the backbones and remove them. Then cut each hen in half along the breastbone. Trim off the wing tips and put the hens in a large bowl.
In a small bowl, combine the 6 Tbs. wine, honey, thyme, bay leaves, and red pepper flakes, and stir to dissolve the honey (it’s all right if it doesn’t dissolve completely).
Using a vegetable peeler, peel the zest from the orange in large strips, letting the strips drop into the bowl with the hens. Add the honey mixture and the sliced onion to the bowl. Toss well, cover, and refrigerate for at least 4 hours or overnight, tossing the hens occasionally.
About half an hour before cooking, remove the hen halves from the marinade and gently pat them dry, trying not to disturb the thyme clinging to them. Arrange the hens on a heavy-duty rimmed baking sheet and let sit at room temperature for 30 minutes. (Discard the remaining marinade.) Position a rack in the top third of the oven and heat the oven to 450°F.
When ready to roast, season the hen halves on both sides with the salt and several grinds of pepper. Turn them skin side up. Roast the hens, basting occasionally with the melted butter and rotating the pan for even browning as needed, until an instant-read thermometer inserted into the meaty part of a thigh registers 175° to 180°F (be careful not to hit the bone), about 30 minutes.
If the skin is somewhat pale, baste the hens, turn the broiler to high, and broil, rotating the pan frequently, until the hens are nicely golden, about 2 minutes. (Watch carefully to prevent burning.) Transfer the hens to a serving platter and tent with aluminum foil.
While the rimmed baking sheet is still hot, add the remaining 1/3 cup wine and use a wooden spoon to scrape the brown bits from the bottom of the pan. Pour the wine and juices into a small saucepan and add the chicken broth. Boil the sauce over high heat until it thickens ever so slightly, 2 to 3 minutes; it should be more like a jus than a thick sauce. Off the heat, whisk in the remaining 1 Tbs. butter. Taste and add salt and pepper, if needed. Keep warm.
To serve, pour a small amount of the sauce on and around the hens and pass the remainder at the table.