Preheat the oven to 375°F.

Spray a 9x13-inch baking dish with nonstick cooking spray. Arrange half the potato slices in the bottom of the dish and season them liberally with salt and black pepper.

Spray a large saucepan with nonstick cooking spray and set it over medium-high heat. Add the beef and diced onion. Saute, breaking up the meat with a rubber spatula as it cooks, until it is browned and the onion is softened, 7-8 minutes. Add the minced garlic, thyme, salt, and black pepper. Continue cooking until the garlic is fragrant, about 1 minute.

Remove saucepan from the heat. Spoon the beef mixture evenly over the potato slices in the casserole dish.

Return the saucepan to the heat and add the butter. Once melted, sprinkle the flour into the pan and whisk to form a paste. Cook for 30 seconds to 1 minute, then slowly pour the half-and-half into the pan, whisking to dissolve the flour.

Cook the sauce, whisking constantly, until it begins to bubble and thicken. Once thickened, turn off the heat. Add the salt and black pepper.

Pour half the sauce over the ground beef mixture. Arrange the remaining potato slices in an even layer on top, and season with more salt and black pepper. Pour the remaining sauce over the potatoes. Sprinkle the shredded cheese evenly over the dish.

Cover the baking dish loosely with aluminum foil.

Bake the gratin on middle rack of oven for 35 minutes.

Carefully remove the aluminum foil and continue baking until the potatoes are fork-tender and the cheese is lightly browned on top, 20-25 minutes.

Check to see that gratin is done. Remove from oven or add time as needed.

Allow the gratin to rest for 10-15 minutes before serving.