Turn on an air circulation and grill oven to 250 degrees C and set the rack on the second to the top position.
An hour before cooking the loins, take them out of the refrigerator.
In a small bowl add the chopped oregano, thyme, 4 tablespoons of olive oil, the balsamic vinegar, 1 teaspoon of salt and one teaspoon of pepper and combine.
Place the loins in a roasting pan, rub the spice/herbs mixture well on them, pressing well on the meat to adhere and put them in the oven for 30 minutes, while tossing halfway through. Check for doneness with an internal thermometer aiming for a temperature of 77 degrees C.
In the meantime, add the shaved asparagus in a small oven-proof dish pan, and toss with the remaining 2 tablespoons of olive oil and ½ teaspoon of salt and ½ teaspoon of pepper. Add in the oven to the lower rack and cook for 10 minutes, while tossing halfway through.
Slice and serve the pork, next to the bulgur and the asparagus. Pour some Hollandaise sauce on the asparagus.