In a large, oven-safe skillet (or Dutch oven), heat the olive oil and butter until melted. Place the pork shoulder in the skillet and season with salt and pepper. Sear on both sides for 3-4 minutes, until browned.
Remove the pork shoulder from the skillet and set aside, keeping the juices in the skillet. Add the onions and carrots to the skillet and sauté until caramelized, about 5-6 minutes.
Add the garlic, thyme, and dry mustard to the onions and carrots. Sauté until the garlic is fragrant, about 2-3 minutes. Season with salt and pepper.
Pour the whiskey into the skillet. Bring to a simmer and allow some of the liquid to evaporate, about 8-10 minutes.
Add the bay leaves, then pour in the chicken broth. Season with nutmeg and brown sugar. Stir and bring to a rolling boil.
Return the seared pork shoulder to the skillet, immersing it in the liquid. Carefully transfer the skillet to the oven and bake at 350°F for 45 minutes to one hour, until the pork is tender and separating from the bone.
While the pork cooks, boil a large pot of water. Add the chopped potatoes and boil for 20-30 minutes, until fork-tender. Drain the potatoes.
In a large bowl, mash the potatoes with three tablespoons of butter and the heavy cream. Season with salt and pepper, to taste. Set aside.
Melt one tablespoon of butter in a small skillet over high heat. Add the remaining chopped onion and sauté until translucent, about 2-3 minutes.
Stir in the cabbage and cook until bright green and crisp, about 3-4 minutes. Remove from the heat and fold into the mashed potatoes. Cover and keep warm until ready to serve.
Carefully remove the pork from the oven. Transfer the pork shoulder to a plate and place the skillet back over high heat. Allow the remaining liquid to simmer for 15-20 minutes, until reduced by more than half (a spoon should leave a trail through the liquid).
Serve the pork shoulder on a pile of colcannon and top with the reduced whiskey sauce. Serve with a glass of whiskey, like a true Irishman. Enjoy!