Prepare a sauce that will also be used for pouring roasted meat: finely chop the onion and garlic. Put them in hot oil and fat and cook until they get a golden color.
After a few minutes, add the finely chopped red pepper, grated orange peel, and the orange juice. Finally, add salt and sugar.
Rub the pork loin with a mixture of salt, thyme powder, fresh rosemary, mint, and hot peppers.
Place the flavored meat in the already hot oven on the rack that you previously greased.
Pour the sauce into a bowl under the rack. During baking, constantly grease the baking with sauce. If the sauce thickens too much, add orange juice.
Bake for about 2 hours. When the pork is well cooked, cut it into finger-thick slices and place on a plate.
Garnish with slices of orange and olive. Drizzle with pre-melted sauce with orange juice and rum. Serve with white rice fried in butter.