Bring a large pot of water to boil over high heat. Add potatoes, cover partially, reduce heat to low and cook until potatoes are tender when pierced with a knife, about 20 minutes.
Meanwhile, in a frying pan over medium-high heat, add bacon and cook until fat has rendered and bacon is crispy, about 15 minutes. Transfer to a paper towel-lined plate to cool. Break into small pieces. Add cabbage and leeks to pan over medium heat, season with salt and pepper and cook until cabbage has softened, stirring occasionally, about 10 minutes.
In a saucepan over medium heat, warm butter and cream.
Using a potato ricer or masher, rice or mash potato quarters into a large bowl. Add butter-cream mixture, all but 1 tablespoon bacon and all but 1 tablespoon green onions. Stir gently to combine. Add cabbage-leek mixture, season with salt and pepper and stir gently to combine.
In a large pot or slow cooker over high heat, add onion, garlic, beer, beef and spices and bring to a boil. Reduce heat to low, cover pot, and cook until tender, 4-6 hours. Strain onions and pickling spices and discard. Reserve corned beef cooking liquid.
To make the vegetables, cut cabbage into 8 wedges. In a separate large, wide pot over medium-high heat, warm oil. When hot, add cabbage wedges and cook until browned, 3-4 minutes. Turn to brown other side. Add carrots and potatoes. Pour in reserved corned beef cooking liquid, increase heat to high and bring to a boil. Reduce to a simmer, cover, and cook for 10-15 minutes. Use tongs or a large spoon to carefully remove cabbage wedges and reserve. Continue cooking carrots and potatoes until cooked through, another 5-10 minutes.
Slice corned beef and serve with cabbage and vegetables. Pour a bit of sauce over corned beef just before serving.
In a large Dutch oven over medium-high heat, add a drizzle of oil, sausage pieces, and bacon and cook until halfway cooked. Transfer half of meat to a plate.
Add half of onion, carrots, and potatoes to pot. Season with salt, pepper, and parsley. Add back other half of meat and remaining onion, carrots and potatoes. Season again with salt, pepper and parsley. Pour broth over meat and vegetables, cover and bake in oven for 1 ½ hours. Remove lid, dot with butter, and continue to cook for 30 minutes.