Preheat the oven to 375°F (190°C).
In a large skillet over medium heat, cook the ground beef, chopped onion, and minced garlic until the beef is browned and the onion is translucent, about 7-8 minutes. Drain excess fat.
Season the beef mixture with salt, black pepper, and dried thyme. Stir well and remove from heat.
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in the milk, continuing to whisk until the sauce thickens and comes to a simmer, about 5-7 minutes.
Remove the sauce from heat and stir in the shredded cheddar cheese until melted and smooth.
Lightly grease a 9×13 inch baking dish.
Arrange half of the sliced potatoes in an even layer on the bottom of the baking dish.
Spread the cooked ground beef mixture evenly over the potatoes.
Pour half of the cheese sauce over the beef layer.
Arrange the remaining sliced potatoes over the sauce layer.
Pour the remaining cheese sauce evenly over the top potatoes.
Sprinkle the grated Parmesan cheese evenly over the top.
Cover the dish tightly with aluminum foil and bake for 45 minutes.
Remove the foil and bake uncovered for an additional 30 minutes, or until the potatoes are tender and the top is golden brown.
Let the casserole rest for 10 minutes before serving.