Preheat grill on high for about 10 minutes. Brush tenderloin with olive oil. Rub with salt and pepper, or seasoning of your choice.
Grill pork with the lid closed, about 7 minutes on each side. Turn off heat and allow pork to cook for another 5 minutes with the lid closed. Pork should reach an internal temperature of 145˚F - 150˚F at its center. Remove from heat and allow to rest for 5 minutes before carving.
Cut pork against the grain into 1/2-inch-thick slices. Create sandwiches by layering on top of buns in this order: 2 slices of cheese, pork, sautéed spinach and then peppers. Serve immediately.