For the Steak
• 3 tablespoons canola or vegetable oil
• 2 tablespoons lemon juice
• 2 tablespoons soy sauce
• 2 tablespoons Worcestershire sauce
• 1 tablespoon Dijon mustard
• 1 tablespoon dark brown sugar
• 1 tablespoon freshly ground black pepper
• 2 teaspoons kosher salt
• 2 teaspoons finely minced garlic (about 2 medium cloves)
• 1 pound flank steak

Garlic-Herb Butter
• 4 tablespoons unsalted butter, softened
• 2 teaspoons finely minced garlic
• 1 teaspoon finely minced chives
• 1 teaspoon finely minced thyme
• 1 teaspoon finely minced parsley
• 1 teaspoon kosher salt

For the Onions and to Serve
• 1 large onion, cut into 1/2-inch slices and skewered horizontally so the rings lie flat on the grill
• 1 tablespoon canola or vegetable oil, for brushing
• Turano French Rolls
• 1/4 pound sliced mild provolone cheese
• 1 large handful arugula

① To prepare the steak: Make marinade by whisking together oil, lemon juice, soy sauce, Worcestershire sauce, mustard, pepper, salt, and garlic in a small bowl. Place steak in a large resealable bag and pour in marinade. Seal bag, removing as much air as possible. Place in refrigerator and let steak marinate for at least 4 and up to 8 hours.
② To make the garlic-herb butter: In a small bowl, whisk together butter, garlic, chives, thyme, parsley, and salt. Set aside.
③ When ready to cook, ignite all burners on grill, close lid, and preheat for 5 minutes. Clean and oil grilling grate. ④ Brush onions with oil and place on grill along with steak. Cook onions until softened and well charred on each side, about 5 minutes per side. Cook steak until it is deeply browned on both sides and an instant-read thermometer registers 125°F when inserted into thickest part of meat (about 3 to 5 minutes per side). Transfer steak and onions to a cutting board as each is done. Let steak rest for 5 minutes, then slice against the grain on a bias. Remove skewer from onions and separate into individual rings.
⑤ Liberally butter cut side of each piece of bread with garlic-herb butter. Place bread on grill, cut side down, and toast until lightly browned, 1 to 2 minutes. Transfer French Rolls to a platter and top half of slices with steak, onions, and cheese.
⑥ Turn off one burner on grill and place topped French Roll slices on cool side of grill. Cover and cook until cheese has melted, about 1 minute. Transfer back to platter and top each sandwich with arugula. Serve immediately.