Prepare a grill fire to about 350° with hickory for smoke flavor.
Pat pork loin dry with paper towels and place on a cutting board.
Starting on the long side, make a thin slice all the way across the loin, and continue to slice in an even layer until pork is in a rectangle, flat layer.
Use a meat mallet and pound until about 1/2 inch thick all over.
Season with 1/2 teaspoon salt and 1/2 teaspoon pepper and set aside.
Thaw spinach and squeeze out excess liquid, coarsely chop.
Place butter in a skillet and place over medium heat. Add spinach, onions, garlic and mushrooms. Cook, stirring often until onions are softened, about 10 minutes.
Spread mixture over pork loin in an even layer.
Starting from the long end, roll up tightly.
Tie loin roast with butcher twine or secure with skewers or toothpicks.
Drizzle with olive oil, rubbing over entire roast.
Sprinkle with dry rub.
Cook over indirect fire with the grill lid closed about 35 minutes. Check with a digital thermometer and continue to cook until loin reaches 145° internal temperature.
Remove from grill and allow to rest about 10 minutes before slicing.
Carefully remove twine and slice into 1/2 inch thick slices.