Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet. Cook, breaking it apart with a spoon, until browned and cooked through, about 6-8 minutes.
Season the beef mixture with salt, black pepper, and dried thyme. Stir well and remove from heat.
Lightly grease a 9×13 inch baking dish.
Layer half of the sliced potatoes evenly on the bottom of the baking dish.
Spread half of the cooked ground beef mixture over the potatoes.
Sprinkle half of the shredded cheddar and mozzarella cheese over the beef layer.
Repeat the layers with the remaining potatoes, ground beef mixture, and cheeses.
Pour beef broth evenly over the entire casserole.
Cover the baking dish tightly with aluminum foil.
Bake in the preheated oven for 45 minutes.
Remove the foil and bake uncovered for an additional 15 minutes, or until the potatoes are tender and the cheese is bubbly and golden.
Remove from oven and let the casserole rest for 5 minutes.
Spread sour cream evenly over the top before serving.