Preheat your Oven to 325°F. Pat the 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes pieces completely dry with paper towels — this is key for a good sear. Season all sides generously with the 1 ½ tsp sal kosher más, ½ tsp pimienta negra molida fresca, and 1 tsp pimentón ahumado.

Heat the 2 tbsp aceite vegetal in a large Dutch Oven over medium-high heat until shimmering. Working in batches if needed, sear the 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes pieces on all sides until deep golden brown, about 3–4 minutes per side. Do not rush this step — the browning builds the flavor base. Transfer seared 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes to a plate and set aside.

If using 2 slices tocino picado aproximadamente, add the chopped 2 slices tocino picado aproximadamente to the same Dutch Oven and cook over medium heat for 2–3 minutes until it begins to render. Add the sliced 1 cebolla amarilla cortada en rodajas finas and cook, stirring occasionally, until softened and lightly golden, about 5 minutes. Add the 4 dientes de ajo aplastados and cook 1 minute more until fragrant.

Stir in the diced 1 manzana pelada, sin semillas y cortada en dados, 1 tsp semillas de alcaravea, 1 tsp tomillo seco, and 1 tbsp azúcar morena comprimida. Cook for 1–2 minutes, scraping up any browned bits from the bottom of the Pot — those bits are pure flavor.

Add the drained 2 can chucrut escurrido, líquido reservado, Chicken Broth Low-Sodium, and Mustard. Stir everything together to combine. Taste the mixture — if it seems very sharp/sour, add a splash of the reserved 2 can chucrut escurrido, líquido reservado liquid later to adjust; if you'd like it milder, discard the liquid.

Nestle the seared 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes pieces back into the Pot, pushing them down into the 2 can chucrut escurrido, líquido reservado mixture so they are at least halfway submerged. The liquid should come about halfway up the 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes. Add a splash of the reserved 2 can chucrut escurrido, líquido reservado liquid if the pot seems dry.

Cover the Dutch Oven with its lid and transfer to the preheated Oven. Braise for 2.5 to 3 hours, until the 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes is completely fork-tender and falling apart. Check once halfway through — if liquid looks low, add a splash of Chicken Broth Low-Sodium.

Remove the pot from the Oven. Carefully lift the 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes pieces out and use two forks to pull the meat into large, rustic chunks, discarding any large bones or excess fat. Return the pulled 3 lb espaldilla de cerdo con hueso cortada en 3–4 trozos grandes to the pot and stir gently to combine with the 2 can chucrut escurrido, líquido reservado.

Taste and adjust seasoning with 1 ½ tsp sal kosher más and ½ tsp pimienta negra molida fresca as needed. Serve hot, garnished with 2 tbsp perejil fresco picado if desired. Classic accompaniments include mashed potatoes, egg noodles, or crusty rye bread.