Pulse the garlic, shallots, coriander, chilli, cumin, 2 tablespoons salt, and 1 teaspoon pepper in a food processor to make a thick paste. Trim the fat on the pork shoulder, leaving only a thin layer of fat. Make deep incisions with a paring knife, at about 10cm intervals, all over the meat. Rub the garlic and spice mixture into and all over the meat.

Combine the lime zest and juice, orange juice, chilli sauce, olive oil, and cinnamon in a nonreactive stainless steel or glass bowl. Add the meat, cover tightly with plastic wrap, making sure the meat is submerged. Refrigerate for at least 8 hours or up 2 days. Bring to room temperature about 1 hour before roasting.

Preheat the oven to 220C. Put the pork, fat-side up, in a large Dutch oven.* Roast the meat, uncovered, for 30 minutes. Add the marinade to the pot and cover with the lid. Lower the temperature to 170C. and roast for 2 hours more. Uncover and continue to cook, basting occasionally, until an instant read thermometer inserted into the meat registers 90 degrees C and the meat is a rich burnished brown, 1 1/2 to 2 hours more. Set aside on a cutting board to rest for 20 minutes before slicing.

For the sauce: Strain the pan drippings through a fine mesh sieve into a gravy separator and discard all excess fat. In a small saucepan, mix the pan drippings with 1/2 cup water and bring to a vigorous boil. Slice the meat and serve with the pan drippings.