Preheat the oven to 425 degrees F. Prepare the pork: Whisk the thyme, rosemary, garlic, mustard and vegetable oil until emulsified. Season with salt and pepper.
Rub the pork liberally with the herb-mustard mixture, then place fat-side up on a rack set inside a heavy-bottomed roasting pan. Roast until the pork is caramelized and a thermometer inserted into the center registers 145 degrees F, 55 to 60 minutes. Transfer to a cutting board and let rest 10 minutes.
Meanwhile, make the sauce: Pour off all but 2 tablespoons drippings from the roasting pan, then heat on the stove over medium heat. Add the mushrooms and cook until caramelized, 6 to 8 minutes. Add the shallots and cook until translucent, about 2 more minutes. Remove the pan from the heat and add the cognac, then return to the heat and scrape up any browned bits from the bottom of the pan with a wooden spoon. Simmer until almost all of the liquid has evaporated. Whisk in the stock, mustard and thyme. Bring to a boil and cook until reduced by half, 8 to 10 minutes. Add the cream and butter and gently boil until thickened. Add the parsley and salt and pepper to taste.
Slice the pork into 12 pieces and drizzle with the sauce.
Make the mayonnaise: Whisk the egg yolks, lemon juice and1 teaspoon salt in a bowl until frothy. Slowly drizzle in the vegetable oil, whisking constantly until completely emulsified.
Make the potato salad: Cook the bacon in a skillet until crisp. Transfer to a paper towel-lined plate to cool, then chop into small bits.
Slice the potatoes 1/4 inch thick; transfer to a pot, cover with water and lightly season with salt. Bring to a simmer over medium heat and cook until just fork tender, 8 to 10 minutes. Drain well.
Combine the bacon, capers, vinegar and chives in a large bowl. Add 1/4 cup mayonnaise (reserve the rest for another use). Gently fold in the warm potatoes and season with salt and pepper.
Cook the bacon in a Dutch oven over medium heat until just crisp. Add the onion and garlic and sweat until translucent, 8 to 10 minutes. Add the cabbage and stir to coat in the rendered bacon fat. Add the vinegar, reduce the heat to low and simmer until the liquid is reduced by three-quarters and the cabbage is tender, about 12 minutes. Add the orange juice and cook until reduced by half, about 5 more minutes.
Remove the cabbage from the heat and fold in the apple. Season with salt and pepper. Serve hot.
Recipe courtesy Jose Garces for Food Network Magazine