Combine the parsley, walnuts and garlic in a food processor and pulse until coarsely chopped. Add the olive oil and process until smooth. Transfer to a bowl and stir in the Pecorino and vinegar and season with salt.
On the bottom half of each sandwich roll, layer 1 ounce provolone, 2 ounces roast beef, 2 teaspoons pesto and 1 tablespoon sun-dried tomatoes. Top with the top half of each roll.
Brush both sides of the sandwich lightly with olive oil. Cook in a panini press until golden on both sides and the cheese melts, about 5 minutes. (Or cook on a griddle or pan with a sandwich weight over medium-high heat and until golden on both sides and the cheese melts, about 5 minutes.)
Leftover pesto can be stored in the refrigerator for up to 3 days (or in the freezer for up to 1 month) with a piece of plastic wrap placed directly on the surface to prevent discoloration.