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 tender, about 7-8 minutes. Drain excess fat.
Season the beef mixture with salt, black pepper, and dried thyme. Stir to combine and set aside.
In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes until lightly golden.
Gradually whisk in the milk, continuing to whisk until the sauce thickens, 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.
Layer the remaining sliced potatoes over the sauce.
Pour the remaining cheese sauce evenly over the top layer of potatoes.
Sprinkle the grated Parmesan cheese evenly over the top.
Cover the baking dish tightly with aluminum foil and bake for 45 minutes.
Remove the foil and bake for an additional 20-25 minutes, or until the potatoes are tender and the top is golden brown.
Let the casserole rest for 10 minutes before serving.