On a clean surface, pat pork dry with paper towels. Using a sharp knife, score skin ⅛-inch deep and ½-inch apart; set aside. Stir together mustard, oil, sugar, rosemary, sage, salt, thyme, garlic, and black pepper in a medium bowl until combined. (Herb mixture will form a paste.) Rub herb mixture evenly over pork. Place pork on a roasting rack fitted inside a large roasting pan, and refrigerate, uncovered, 12 to 16 hours.

Preheat oven to 250°F. Remove pork from refrigerator, and let stand at room temperature while oven preheats. Bake pork in preheated oven until a thermometer inserted into thickest portion of pork registers 180°F (sliceable) to 195°F (fall-apart), 8 to 10 hours. Remove pork from oven, and transfer rack and pork to a large, rimmed baking sheet, reserving drippings in roasting pan; tent pork with aluminum foil, and let stand at room temperature 30 minutes. While pork is resting, prepare the Shallot Pan Sauce

Pour drippings from roasting pan through a fine mesh strainer into a small heatproof bowl. Reserve 2 tablespoons drippings; discard remaining drippings or store in an airtight container in refrigerator for another use. Set roasting pan aside until ready to use; do not wipe clean. Whisk together cornstarch and 2 tablespoons of the stock in a small bowl until combined; set aside until ready to use.

Place roasting pan over 2 burners; add reserved 2 tablespoons drippings to roasting pan, and heat over medium-high. Add shallots to drippings, and cook, stirring constantly, until softened and starting to crisp up on edges, about 2 minutes. Add wine, and cook, stirring often with a wooden spoon to scrape up browned bits on bottom of pan, until liquid is reduced by half, about 7 minutes. Add remaining 3 cups stock, and bring to a simmer over medium-high. Cook, stirring occasionally, until reduced to about 2 cups, 7 to 8 minutes.

Reduce heat to a medium-low to maintain a gentle simmer; whisk in butter and mustard until combined. Whisk in cornstarch slurry until combined, and cook over medium-low, whisking occasionally, until sauce is thickened to desired consistency, 2 to 3 minutes. Season to taste with a few grinds of black pepper, and pour into a sauceboat.

Slice or pull apart pork, and serve with Shallot Pan Sauce. Garnish with fresh thyme leaves.