Check the bone side of the ribs. If there is a thin membrane covering them (called silverskin), loosen it with a paring knife and peel it off with your fingers to make them easier to slice. Put the ribs in a baking sheet and spread the seasoning rub all over both sides of the ribs. Refrigerate uncovered for at least 8 hours and up to 48 hours.
When you’re ready to barbecue, heat the grill to 250°F to 275°F. Turn off all but the far left burners. Put the ribs bone-side-down on the unlit side of the grill, close the lid, and cook for 2 hours until the meat registers an internal temperature of 165°F to 175°F.
Meanwhile, combine the tamarind syrup with ½ cup of the pineapple in a bowl.
Remove the ribs from the grill and place them, meat side up, on a large piece of aluminum foil. Pour half the tamarind syrup mix over them. Flip the ribs to meat side down and pour the remainder of the tamarind mix. Place the cubes of butter under and on top of the ribs. Close the foil packet tightly.
Return the packet to the grill, meat side down, close the lid, and cook for 2 hours until meat reaches an internal temperature of 205°F. Remove from the grill and let the meat rest, still wrapped in the foil, for at least 15 minutes so the juices reabsorb. Remove from the foil, cut the rack into double or individual ribs.
Optionally, grill some pineapple slices until caramelized and serve with the ribs. Serve hot and finish with a sprinkle of cotija cheese and garnish with parsley leaves.