Step 1

Position an oven rack in the top third of the oven and preheat to broil.

Step 2

Lightly grease the left third of an 18-by-13-inch sheet pan with the butter.

Step 3

Mix the Parmesan, heavy cream, thyme, garlic, 1 teaspoon salt and a few grinds of black pepper in a medium bowl. Add the potatoes and toss to coat.

Step 4

Arrange the potatoes in even overlapping layers on the buttered part of the sheet pan. Pour whatever cream mixture remains in the bowl on top. Sprinkle evenly with the Gruyere.

Step 5

Brush oil on both sides of the steak and sprinkle generously with salt and pepper. Put the steak on the middle third of the sheet pan. Broil for 5 minutes to begin browning the potatoes and steak. Meanwhile, put the shrimp scampi in a 1 1/2-quart oval baking dish.

Step 6

Remove the sheet pan from the oven, lower the oven to 450 degrees F and put the baking dish with the shrimp on the right third of the sheet pan next to the steak. Return the sheet pan to the oven and bake, stirring the shrimp halfway through, until the shrimp are cooked and the steak registers 135 degrees F for medium-rare, 16 to 18 minutes.

Step 7

Remove the steak to a cutting board and allow to rest for 10 minutes. Slice and serve the steak with the potatoes, shrimp scampi, spinach salad and bread for sopping up the flavorful juices.