In a small bowl, mix together 1 tablespoon of salt, sugar, oregano, 1 teaspoon of black pepper, white pepper, and cayenne. Rub the mixture over tenderloins to coat.
In a straight-sided oven-proof skillet large enough to fit the entire length of the loins, heat 2 tablespoons of the oil over medium heat. When hot, add the pork loins and sear on all sides until just golden, about 2 to 3 minutes each side. (Depending on the size of the skillet, you may need to sear in batches.) Transfer to the oven and bake until the internal temperature reaches 145 degrees F on an instant-read thermometer, about 20 to 25 minutes. Remove the skillet from the oven and transfer the roasts to a cutting board. Loosely cover with aluminum foil and let rest 10 minutes.
Heat the skillet over medium heat, add the remaining oil, the onions, pineapple and garlic. Saute until the pineapple caramelizes slightly. Add the red pepper flakes and saute a few minutes more. Stir in the spinach and season with salt and pepper, to taste. Add broth, cover and cook the spinach until it wilts. Slice the pork and arrange on a serving platter. Serve with the greens and pineapples.