Cut the pork shoulder into chunks suitable for your grinder. In a bowl, mix the meat with salt, garlic, pepper, and cumin. Cover and refrigerate overnight or up to 2 days.

Soak the sheep casings in warm water for about 30 minutes, then optionally flush them with water to clean.

Grind the meat mixture through a medium die. Chill the mixture until it reaches about 33°F.

In a small bowl, mix the achiote paste with the Seville orange juice. Combine this mixture with the meat and mix well until the sausage is cohesive.

Stuff the sausage into the casings, leaving enough space at the ends for tying off.

Tie off the ends of the sausage and hang it to dry at room temperature for 1-2 hours. Ideally, store it in a cooler environment between 33-39°F for 24 hours or up to 3 days.

Optional: For extra flavor, smoke the longaniza after it has hung for a day. Cook it at a temperature under 200°F until the inside reaches 150°F.