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1
Set oven to 400 F. Rinse the neck bones and pat dry. Line a rimmed baking sheet with foil and set a wire rack in it. Season the bones with salt and pepper and set on the rack, then roast in the oven 60 minutes, turning the bones over halfway through. Remove from oven, cover with foil, and set aside. Lower heat to 250 F.
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2
Toast whole seeds briefly in a dry skillet. Let cool, then transfer to a mortar or spice grinder. Blitz with the remaining herbs, the kosher salt, the juniper berries, and the sugar. Combine with the sweet and hot paprika, then whisk in a large bowl with the tomato paste, lecso, vinegar, and Worcestershire sauce. Set aside.
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3
Rinse the pork butt and pat dry. Do the same with the belly. Season with salt and pepper. Heat oil in a large, heavy-bottomed skillet or saute pan. Brown butt/shoulder and belly pieces all over, working in batches and transferring browned pieces to a large bowl to catch all their juices. When all the pork is browned, toss the belly, butt/shoulder pieces, and any accumulated juices in the bowl with the spice paste. Spread the roasted neck bones in the bottom of a large casserole or 9 x 13 baking dish. Smother with the spice-paste-coated pork, scraping down the sides and bottom of the bowl so every last bit of paste makes it into the baking dish. Cover the dish tightly with foil, secure with the lid, and braise in the oven 4 hours. At about the halfway mark, your kitchen will start to smell amazing.
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4
Remove the casserole from the oven. Uncover (taking care to avoid steam-burning yourself!). Remove the pork from the sauce with a slotted spoon or tongs and prepare each component for storage separately. You can also take this opportunity to separate the neck meat from the bones--either discard or reserve them for stock. When both pork and sauce have cooled to room temperature, refrigerate them until ready to use again.
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5
If the sauerkraut is very fresh, simmer in water until tender, then drain and set aside. Take the pork and its sauce from the refrigerator. Let the pork come to room temperature. (The reserved sauce should have congealed and have a consistency like that of refrigerated gravy.) If a fat cap has formed on the surface of the sauce, remove it. (If there is a significant amount of fat, reserve a little for sauteing and discard the rest, or reserve for another use.)
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6
Heat 2 tbsp fat or oil (or a mix of both) over medium-low heat until shimmering. Add the onions and garlic and saute until tender and translucent and turning golden. Remove from heat and add the paprika, caraway, and water, and whip to integrate. Return the pan to heat and add the tomatoes and their juice, the pork, and the sauce. Mix in the sauerkraut and the peppers and bring to a simmer. Then cover, lower the heat, and stew for 30 minutes.
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7
Toss warm noodles, potatoes, or spaetzle with a spoonful of the reserved fat or some butter or oil and divide among bowls. Spoon the goulash over and top each with a dollop of sour cream and a sprinkle of paprika.
