1) Heat the oven
Preheat to 325°F.
2) Make the achiote marinade
In a blender or food processor, combine achiote paste, orange juice, lime juice, vinegar, garlic, salt, cumin, oregano, cinnamon, and cloves. Blend until smooth. If your achiote paste is stubborn, give it a minute to sit in the citrus, then blend again.
3) Coat the pork
Put the pork chunks in a bowl (or right in your Dutch oven) and pour the marinade over. Toss until every piece is thoroughly coated. Let it sit while you prep the onions, or cover and refrigerate up to 24 hours for even deeper flavor.
4) Start the pickled onions
Add sliced onions to a heat-safe bowl or jar. In a small saucepan (or microwave-safe bowl), combine vinegar, warm water, sugar, salt, and any optional spices. Heat just until the sugar and salt dissolve, then pour over the onions. Press onions down so they are mostly submerged. Let sit at room temp while the pork cooks, then refrigerate.

5) Slow roast
Add broth (or water) and bay leaf to the Dutch oven. Nestle the pork in, ideally in a snug single layer if your pot allows. If one side has a thicker fat cap, set that side up. Scrape any remaining marinade into the pot, then cover tightly with the lid.
Roast for 3 hours, turning the pork once halfway through if you remember. It’s ready when it’s fork-tender and practically shredding itself. If you like numbers, aim for about 195 to 205°F in the thickest part, but tenderness is the real test.
6) Shred and season to taste
Remove the bay leaf. Shred the pork directly in the pot using two forks. Taste and adjust with a pinch more salt, a squeeze of lime, or a splash of vinegar if you want it brighter.
If your shoulder rendered a lot of fat, you can skim it off the top, or chill the pot briefly and lift off the solidified fat.
If you want slightly thicker juices, simmer uncovered on the stovetop for 5 to 10 minutes, stirring occasionally.

7) Serve
Serve in warm tortillas with pickled onions, cilantro, and lime. For extra texture, crisp a portion of the shredded pork in a hot skillet for 3 to 5 minutes until the edges catch.