After grilling, marinate the sliced steak in arugula chimichurri for an extra-fresh finish, then layer it on top of brie.
Preheat a grill or grill pan to medium-high. Rub steak with brown sugar; season with salt and pepper. Let stand 10 minutes. Pulse arugula and parsley in a food processor until finely chopped. Transfer mixture to a bowl; stir in vinegar, oil, 1/4 teaspoon salt, and brine.
Lightly brush grill with oil. Pat steak dry; grill, turning once halfway through, until well browned (7 to 9 minutes total for medium-rare). Let stand 10 minutes, then slice 1/4 inch thick against the grain. Toss with accumulated juices, peppers, and half of chimichurri. Drizzle baguette halves with oil; grill, turning once, until lightly toasted, 1 to 2 minutes. Just before serving, layer bottom half of baguette with brie and steak mixture. Top with arugula; close sandwich and cut into 4 portions. Serve, with remaining chimichurri.