Preheat the oven to 375°F (190°C).
Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook until translucent, about 3-4 minutes.
Add the minced garlic and cook for another 30 seconds until fragrant.
Add the ground beef to the skillet. Cook, breaking it apart with a spoon, until browned and cooked through, about 7-8 minutes.
Season the beef mixture with salt, black pepper, dried oregano, and dried thyme. Stir well and remove from heat.
In a small saucepan, melt the butter over medium heat. Stir in the flour and cook for 1-2 minutes, stirring constantly to form a roux.
Gradually whisk in the milk and beef broth. Continue to whisk and cook until the sauce thickens, about 3-4 minutes. Remove from heat.
Spread half of the sliced potatoes evenly in the bottom of a greased 9×13 inch baking dish.
Layer half of the cooked ground beef mixture over the potatoes.
Pour half of the milk sauce evenly over the beef layer.
Sprinkle half of the shredded cheddar and mozzarella cheeses over the sauce.
Repeat the layers: remaining potatoes, remaining ground beef, remaining milk sauce, and finish with the remaining shredded cheeses on top.
Cover the casserole dish with aluminum foil and bake in the preheated oven for 40 minutes.
Remove the foil and bake for an additional 15-20 minutes, or until the cheese is golden and bubbly and the potatoes are tender when pierced with a fork.
Remove from the oven and let the casserole rest for 5 minutes before serving.