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1
Bring 6 cups water, 1/4 cup kosher salt, 1/4 cup brown sugar, whole allspice, and bay leaves to boil in large saucepan, stirring to dissolve salt and brown sugar.
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2
Cool brine completely in refrigerator; add pork chops and refrigerate overnight.
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3
Heat olive oil in heavy large saucepan over medium-high heat.
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4
Add sliced red onion and saute 2 minutes.
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5
Stir in bay leaf, sage sprig, and dried crushed red pepper.
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6
Add sliced red cabbage and cook until wilted and crisptender, stirring often, about 10 minutes.
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7
DO AHEAD: Can be made 2 hours ahead.
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8
Let stand at room temperature.
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9
Preheat oven to 300F.
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10
Remove pork chops from brine; pat dry.
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11
Season lightly with salt and generously with ground black pepper.
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12
Heat olive oil in heavy large ovenproof skillet over high heat.
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13
Cook pork chops in skillet until browned, about 3 minutes per side.
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14
Transfer skillet to oven and cook until thermometer inserted horizontally into pork chops registers 145F, about 7 minutes.
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15
Transfer pork to plate (do not clean skillet).
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16
Add chicken broth, beef broth, thyme sprig, sage leaves, rosemary sprig, and parsley sprig to skillet and boil until liquid is reduced to 1/2 cup, about 9 minutes.
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17
Discard herbs.
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18
Whisk in 1 teaspoon chopped sage and 1 tablespoon butter.
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19
Keep warm.
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20
Rewarm cabbage.
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21
Stir in remaining 2 tablespoons butter and 2 tablespoons red wine vinegar.
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22
Season to taste with salt and pepper.
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23
Divide cabbage among plates.
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24
Place 1 pork chop on each plate.
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25
Drizzle pork with sauce and serve.
