Make the marinade: whisk together soy sauce, lime juice, Worcestershire sauce, olive oil, minced garlic, sugar, and freshly ground black pepper in a medium bowl.
Place the flank steak in a large resealable plastic bag (or shallow dish) and pour in the marinade, removing excess air and sealing the bag; refrigerate for at least 6 hours or up to 24 hours, turning the bag occasionally.
Preheat your grill to medium-high heat while the steak finishes marinating.
Remove the steak from the marinade and discard the leftover marinade.
Grill the steak 5 to 7 minutes per side for medium, adjusting time for your preferred doneness.
Transfer the steak to a cutting board and let it rest 10 minutes; while it rests, butter the hoagie buns with the optional butter and toast cut-side down on the grill.
Prepare the chimichurri mayonnaise by mixing chimichurri sauce with mayonnaise (can be made up to 24 hours ahead).
Slice the rested steak thinly against the grain.
Assemble sandwiches: spread chimichurri mayonnaise on each bun, add several slices of steak, top with sliced tomatoes (season lightly with salt and pepper) and arugula, then serve immediately.