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1
Preheat the oven to 400.
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2
Season the pork all over with salt and pepper.
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3
In a large skillet, heat the oil until shimmering.
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4
Add the pork roast and cook over moderately high heat, turning, until browned all over, about 12 minutes.
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5
Transfer the pork to a 12-by-14-inch roasting pan.
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6
Pour off all of the fat from the skillet.
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7
Add the honey and cook over moderate heat, stirring, until it turns a deep amber, 3 to 5 minutes.
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8
Stir in the soy sauce, then add the demiglace and chicken stock and bring to a boil.
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9
Pour the liquid over the pork and roast for about 50 minutes, basting every 10 minutes, until an instant-read thermometer inserted in the thickest part of the meat registers 120; add 1/4 cup of stock or water to the roasting pan if the juices evaporate too quickly.
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10
Scatter the carrots, turnips and brussels sprouts around the pork and roast for about 25 minutes longer, basting occasionally, until the pork is glazed and an instant-read thermometer inserted in the thickest part registers 150.
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11
Transfer the pork roast to a carving board, tent it with foil and let it rest.
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12
Return the roasting pan to the oven and roast the vegetables for 20 to 25 minutes longer, until tender.
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13
Using a slotted spoon, transfer the vegetables to a medium bowl.
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14
Pour the pan juices into another smaller bowl or a gravy boat.
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15
Thinly slice the pork and serve with the pan juices and vegetables.
