Preheat the oven to 300°. In a large skillet, heat 1 tablespoon EVOO, 1 turn of the pan, over high heat. Add the ground beef and cook, breaking it up, until browned, about 7 minutes. Season the meat with the paprika and salt and pepper to taste. Keep warm over low heat.
Meanwhile, make the chimichurri: Using a food processor, pulse together the onion, garlic, parsley, vinegar, oregano, thyme and rosemary until finely chopped. With the machine on, pour in the remaining 1/3 cup EVOO.
In a small bowl, combine the tomato sauce, Worcestershire sauce and brown sugar. Stir into the meat and bring to a simmer. Stir in half of the chimichurri and cook for 5 minutes.
Warm the rolls in the oven. Split them and slather the cut sides of the tops with the remaining chimichurri. Pile the meat onto the bun bottoms, cover with the tops and serve.