If you don't want to butterfly the pork loin yourself, ask your butcher to do it for you.
Preheat the oven to 400°. Cut the center stems from the chard. Coarsely chop enough stems to measure 1 1/2 cups. Transfer to a food processor. (Discard the remaining stems.) Thinly slice the chard leaves; transfer to a large bowl. To the processor, add the parsley, pistachios, cheese, shallot, and lemon juice; pulse until coarsely chopped. With the machine running, gradually add 1/2 cup EVOO. Season the pesto with salt and pepper. Transfer 3 tbsp. of the pesto to a small bowl. Whisk in 3 tbsp. EVOO to make the dressing. Cover and refrigerate the chard and dressing separately.
Place the roast, fat-side down, on a work surface. Using a sharp long knife, cut into 1 long side of the roast about 1/2 inch from the bottom. Continue cutting, unrolling the roast like a carpet. Spread the remaining pesto on top, leaving a 1-inch border. Roll up the roast; using kitchen twine, tie it in 6 places. Season the outside of the roast.
In a large roasting pan set over 2 stovetop burners, heat the vegetable oil over medium-high. Add the roast. Cook, turning often, until browned, 5 to 10 minutes. Transfer to the oven. Roast until an instant-read thermometer registers 145° when inserted into the center, about 50 minutes. Let rest for 15 minutes. Cut the roast into 1/2-inch slices.
Toss the sliced chard, chile, and half the dressing; season. Transfer to a platter. Arrange the roast on top. Drizzle the remaining dressing over the roast.