1 head garlic (about 10 cloves)

½ cup mayonnaise

¼ cup Italian dressing

1 flank steak (1½ to 2 pounds)

Kosher salt

¼ cup olive oil, plus more for grilling

¼ cup balsamic vinegar

2 pounds Yukon Gold potatoes

1 stick unsalted butter

1 pound broccoli florets

1 teaspoon crushed red pepper

1 12-ounce loaf soft French bread

6 slices provolone cheese

Preparation: 

Using a mallet or the back of a knife, carefully crack apart the garlic cloves. Remove the peels, then smash the cloves.

Mince 1 clove of the smashed garlic. In a small bowl, whisk together the mayonnaise, Italian dressing, and minced garlic, then set the sauce aside for later.

Season the flank steak with kosher salt on all sides. Transfer the steak to a large resealable plastic bag, then add ¼ cup of olive oil, the balsamic vinegar, and 6 of the smashed garlic cloves. Seal the bag and massage the steak to combine all the ingredients. Set the steak aside to marinate.

While the steak marinates, place the potatoes in a large pot, then cover them with water and heavily salt the water. Bring the water to a boil over high heat, then cook the potatoes until fork-tender, 20 minutes.

While the potatoes cook, melt the butter in a medium pan over medium-high heat. Add the remaining smashed garlic cloves and reduce the heat to medium. Cook until the garlic is just beginning to turn golden, about 10 minutes, then set the garlic butter aside to cool.

Once the potatoes are tender, drain and transfer them to a baking sheet. Using the bottom of a glass, gently smash the potatoes on the baking sheet, then set them aside to cool.

While the potatoes cool, in a large bowl, toss the broccoli with enough of the garlic butter to coat, then season with the crushed red pepper and a pinch of salt.

Heat a gas or charcoal grill over medium-high heat for two-zone cooking. Drizzle the smashed potatoes with olive oil, then place them on the grill over direct heat and cook until charred and crispy on 1 side, about 3 minutes. Flip the potatoes and cook until charred on both sides, 2 minutes more. Transfer the potatoes to the indirect heat to keep them warm and brush with the remaining garlic butter.

Grill the broccoli over direct heat, turning as needed, until charred, about 3 minutes total. Transfer the broccoli to a serving plate.

Remove the steak from the marinade and pat it dry with paper towels. Transfer the steak to the grill and cook over direct heat, flipping frequently, until charred and cooked to your desired doneness, about 15 minutes for medium-rare steak. Transfer the steak to a plate and set it aside to rest.

Split open the loaf of bread. Coat both sides with the sauce, then top with the cheese. Thinly slice the rested steak against the grain, then place it on top of the cheese (don’t close the sandwich yet). Return the sandwich to the grill to melt the cheese, 1 minute more.

Remove the sandwich from the grill. Close the sandwich and slice it into 4 servings. Serve the sandwiches with broccoli and smashed garlic potatoes.