Remove stems and seeds from dried chiles. Heat a Dutch Oven over medium-high and add chiles and toast, turning frequently, until fragrant and darkened, 1–1 ½ minutes.

Pour chicken stock over chiles to halt toasting. Bring to a brief boil, then remove from heat. Cover Dutch Oven and let chiles soften for 30–60 minutes.

Transfer rehydrated chiles to a blender and let cool slightly. Add 3 cups of the soaking liquid and blend until smooth. Transfer remaining soaking liquid to a bowl and set aside.

Wipe out Dutch Oven and heat over medium-high with oil. Season pork generously with salt and pepper. Working in batches to avoid overcrowding the pot, brown pork, 5–7 minutes per batch. Transfer to a Sheet Pan or Platter. (You're not trying to cook it through, just browning the exterior of the pork for good flavor.)

Remove Dutch Oven from heat. Add garlic and sage and cook, stirring, until fragrant, about 1 minute. Add cumin and oregano. Add about 1 cup reserved soaking liquid and return Dutch Oven to medium heat. Deglaze the bottom of the Dutch Oven, scraping with a Wooden Spoon to remove browned bits.

Return pork to Dutch Oven. Add chile puree, bay leaves, and remaining soaking liquid. Bring to a boil, reduce heat to medium, and simmer covered until pork is very tender, 40–60 minutes. Check pork as it cooks and adjust heat to maintain a simmer, if needed. Alternatively, bake, covered, in a 225F oven for 6–8 hours.

Remove lid and simmer uncovered for 10 minutes more, until the concoction is a beautiful, thick, smooth mahogany color. The sauce should be thick enough to coat the back of a spoon. Taste and season with salt and pepper, as needed.

Serve topped with a sprinkle of flaky salt, sliced red onion, cilantro, lime wedges, and tortillas.