GRILL THE PORK: Prepare the grill for direct cooking over medium heat (350 – 450 degrees F). Pat dry the tenderloin and remove, if necessary, the silver skin (connective tissue) with a small sharp knife. Brush the pork with oil and sprinkle all over with 1 teaspoon kosher salt, ½ teaspoon fresh ground pepper, and 2 tablespoons minced fresh or 1 tablespoon dried (rub between your fingers before using) rosemary, pressing the spices into the meat. Grill the pork over direct medium heat with the lid closed, turning twice, until the outsides are evenly seared and an instant read thermometer inserted into the center registers 145 degrees F – about 20 minutes. Let pork rest 3-5 minutes. Slice thinly. (If one end of the tenderloin is very thin, tuck it under and secure it with toothpicks or a skewer so that it doesn’t overcook.)
SAUTÉ MUSHROOMS + ASPARAGUS WITH ONION/GARLIC: While the pork cooks, heat a large heavy skillet over medium-high flame and add 2 tablespoons olive oil. When the oil is quite hot, stir in the mushrooms, asparagus, and onion. Season with a ¼ teaspoon each kosher salt and fresh ground pepper. Cook, stirring, for 5 minutes or until just barely tender, adding the garlic for the last minute. Remove skillet from heat and set aside.
DRESS THE GREENS: When the pork is cooked and resting, add the arugula to a large bowl and sprinkle with salt and pepper. Drizzle lightly with lemon vinaigrette and toss gently and thoroughly. Taste and adjust seasonings or add a bit more vinaigrette if needed.
ARRANGE FOR SERVING/GARNISH: Place the dressed arugula evenly around the outside of the platter. Carefully add the pork to the center of the greens and spoon the asparagus mixture around the meat. Down the center of the tenderloin, place the diced tomato and then the minced parsley on top of that. Serve while meat is warm, passing a small pitcher of the lemon vinaigrette at the table.