Cover the dried ají colorado chiles with boiling water in a bowl and soak until softened, 20–30 minutes; drain, reserving 1 cup of the soaking liquid.
Blend the softened chiles with garlic, ground cumin, dried oregano, white vinegar, and 0.5 cup of the reserved chile soaking liquid until very smooth, 1–2 minutes; add more soaking liquid as needed to make a thick, pourable paste.
Put the pork shoulder in a large pot, add the salt, and cover with cold water by about 1 inch. Bring to a simmer, skimming foam, then cook gently until the pork is tender but not falling apart, 60–75 minutes. Lift the pork out and reserve 2 cups of the cooking liquid.
Heat the lard in a wide heavy pot over medium-high heat until shimmering. Add the drained pork and fry, turning occasionally, until lightly crisped and browned on the edges, 8–10 minutes; transfer the pork to a plate, leaving the fat in the pot.
Add the yellow onion to the same pot and cook, stirring, until translucent and sweet, 5–7 minutes.
Stir in the chile paste and cook it down, stirring often, until thick, glossy, and brick red, 8–10 minutes.
Pour in 1.5 cups of the reserved pork cooking liquid, stirring to loosen the paste, and simmer until the sauce is smooth and lightly thickened, 8–10 minutes.
Return the browned pork and any juices to the pot, toss to coat in the sauce, and simmer on low until the meat is well glazed and tender and the sauce clings, 12–15 minutes. Adjust seasoning with additional salt if needed.
While the pork cooks, place the soaked dried white hominy (mote pelado) in a pot, cover with fresh water by 2 inches, bring to a boil, then reduce to a gentle simmer and cook until the kernels are plump and tender, 1.5–2 hours; drain and keep warm.
In a separate pot, cover the yellow potatoes with cold salted water, bring to a boil, and cook until just tender when pierced, 20–25 minutes; drain. Peel if desired.
Serve generous spoonfuls of mote on each plate, add the potatoes, and top with the pork and plenty of the ají colorado sauce. Serve hot.