Preheat the oven to 325 degrees F. Trim the fat cap on the corned beef to about 1/4 inch thick, then rinse the corned beef. Place in a large Dutch oven and cover with water by 1 inch. Bring to a boil, then turn off the heat and skim off any foam from the top. Transfer the beef to a plate, discard the water and wipe out the pot. Combine the allspice, peppercorns, bay leaves, thyme and garlic on a large square of cheesecloth. Gather the edges to make a bundle, tie with kitchen twine and set aside.
Return the beef to the pot. Add the cheesecloth bundle, cider, whiskey and 4 cups water. Bring to a boil, then reduce the heat so the liquid simmers. Cover, transfer to the oven and bake 1 1/2 hours. Remove the pot from the oven and flip the beef; cover and continue baking until tender, about 1 1/2 more hours.
Line a rimmed baking sheet with parchment paper. Transfer the pot to the stovetop and increase the oven temperature to 400 degrees F. Remove the beef from the liquid and place on the prepared baking sheet, fat-side up; reserve the pot of liquid.
Whisk the mustard, brown sugar, honey and horseradish in a bowl. Brush 1/4 cup of the mustard glaze on the corned beef. Return to the oven and bake until the glaze is lightly browned and sticky, about 15 minutes. Brush with the remaining glaze and bake 15 more minutes. Remove from the oven and let rest 10 minutes.
Meanwhile, bring the liquid in the pot to a boil. Add the rutabaga and reduce the heat so the liquid simmers; cook until the rutabaga is very tender, about 20 minutes, adding the leeks halfway through. Transfer the vegetables to a platter using a slotted spoon. Slice the corned beef and arrange on the platter; sprinkle the vegetables with parsley.