Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat.
Add chopped onion and minced garlic to the skillet and sauté for 3-4 minutes until softened.
Add ground beef to the skillet and cook until browned, breaking it up with a spoon, about 6-8 minutes.
Season the beef mixture with salt, black pepper, dried oregano, and dried thyme. Stir well and remove from heat.
In a large mixing bowl, combine the thinly sliced potatoes with beef broth and sour cream. Mix until potatoes are evenly coated.
In a greased 9×13-inch casserole dish, spread half of the potato mixture evenly on the bottom.
Layer half of the cooked ground beef mixture over the potatoes.
Sprinkle half of the shredded cheddar and mozzarella cheeses over the beef layer.
Repeat layering with the remaining potato mixture, ground beef, and cheeses.
Cover the casserole dish tightly with aluminum foil and bake in the preheated oven for 45 minutes.
Remove the foil and bake uncovered for an additional 15 minutes, or until the cheese is bubbly and golden and the potatoes are tender when pierced with a fork.
Remove from oven and let the casserole rest for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.