Beef Burgers with Mushrooms and Aioli

Combine the ground chuck , salt, and pepper in a medium bowl. Shape the mixture into 4 (1/2-inch-thick) patties.

Lightly drizzle both sides of the mushrooms with the oil. Sprinkle with salt and pepper.

Mix the mayonnaise, lemon juice , and garlic in a small bowl to blend . (The patties, mushrooms, and garlic mayonnaise can be prepared up to this point 1 day ahead. Cover them separately and refrigerate.)

Prepare the barbecue (medium-high heat). Grill the burgers until cooked to desired doneness, about 4 minutes per side for medium-rare. Grill the mushrooms until just tender, about 5 minutes per side. Grill the focaccia squares cut side down, until lightly toasted, about 2 minutes.

Spread the garlic mayonnaise over the roll bottoms. Cut the mushrooms into strips and arrange the mushroom strips over the mayonnaise . Place the burgers atop the mushrooms. Spread garlic mayonnaise on the cut side of the tops and arrange a handful of arugula on each. Cover the burger with the roll tops and serve.