Make the spice rub: In a small skillet, heat the coriander and cumin seeds over medium, swirling the skillet, until toasted, 3 minutes. Transfer the seeds to a spice grinder and process until finely ground. Pour the spices into a bowl and stir in the dried thyme, paprika, and allspice.
Place the pork shoulder, fat side up, in a 9-x-13-inch baking dish and, using a paring knife, score the fat in a 1⁄2-inch-deep crosshatch pattern. Rub the pork with the vegetable oil and then season liberally with salt and pepper. Sprinkle the spice rub on the pork and rub it all over until evenly coated. Cover the pork with plastic wrap and refrigerate at least 12 hours.
Heat the oven to 300°. Remove the plastic wrap and then tightly cover the pork shoulder with foil. Bake until the pork is very tender when pierced with a knife, about 4 to 5 hours
Meanwhile, make the parsley bagna cauda: In a small saucepan, combine the milk and garlic, and bring to a boil over high heat. Reduce the heat to maintain a simmer and cook until the garlic is tender when pierced with a knife, about 15 minutes. Remove the pan from the heat and, using a slotted spoon, transfer the garlic to a work surface. Reserve the garlic-infused milk and peel the garlic.
With a mortar and pestle or food processor, mash the garlic cloves with the parsley, anchovies, and 1⁄2 teaspoon salt until smooth. Stir in 1 tablespoon of the garlic milk, the olive oil, butter, lemon juice, and vinegar and then spoon the bagna cauda into a serving bowl
When the pork is tender, remove it from the oven and increase the temperature to 425°. Remove the foil and drain off the pan juices into a bowl. Let the juices stand to separate, then skim off and discard the fat. Return the pork to the oven and roast until the pork turns dark golden brown and the top is crisp, 15 to 20 minutes. Pour the pan juices back into the baking dish, shred the pork with two forks, and serve with the parsley bagna cauda.