Remove all the outer extra fat and pork filaments from each tenderloin. Butterfly each tenderloin once in the middle, making sure you leave about ½ inch of meat space between the knife and the cutting board and not going through. Once the tenderloins are halved, butterfly it three more times from each side starting in the middle. You will have cut down alongside the tenderloin seven times, making sure you never cut through the meat. Each piece of pork tenderloin will be 7 to 8 inches wide. Pound the pork lightly. Season with salt and pepper generously the inside.
Preheat the oven to 375F.
Arrange the arugula on top of the cut side of each tenderloin, grind a generous amount of pepper over it. Arrange the slices of mozzarella over the arugula and sprinkle with salt and pepper. Add the basil leaves and again sprinkle with a generous amount of pepper.
Roll each tenderloin, ensuring the arugula and mozzarella are tucked in. Using cooking twine, tie in 4 to 5 places. Place a couple of toothpicks at each end to seal them. Sprinkle a generous amount of salt and pepper all over them. You will have two pork tenderloins rolls.
Place a large ovenproof skillet over medium-high heat and add the olive oil. Once hot but not burning, add the pork tenderloins rolls and sear each side until a nice medium brown crust is formed. Do not always turn as you want a nice searing to take place.Once all the sides, 5 to 8 minutes, are golden, place the skillet in the hot oven—Bake for 30 to 40 minutes.
Remove from the oven and place the tenderloins on a plate with a bit of high border to hold on any juice rendered and cover with aluminum foil.Return the skillet to the stove, add two tablespoons of butter, the shallots, and parsley. Sauté the shallots for a couple of minutes until slightly translucent. Lower the heat and add the red wine, deglazing by scraping the pan for any bits. Raise temperature back to medium and reduce the wine to 1/3. Add the heavy cream and stir sauce together. Add the remaining butter to the skillet and continue to stir until melted and season with salt and pepper to taste. Add any juices rendered by the tenderloins.
Cut the pork tenderloin into 1-inch thick slices and serve with the sauce over it or alongside.