Preheat the oven to 350°F (175°C).
Cook the egg noodles according to package instructions until al dente. Drain and set aside.
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 sliced mushrooms to the skillet. Cook for an additional 4-5 minutes until mushrooms are tender.
Add ground beef to the skillet. Cook, breaking it up with a spoon, until browned and cooked through, about 6-8 minutes. Drain excess fat.
Stir in frozen peas, Worcestershire sauce, dried thyme, salt, and black pepper. Cook for 2 minutes more.
In a large mixing bowl, combine the condensed cream of mushroom soup, sour cream, and milk. Mix until smooth.
Add the cooked ground beef mixture and cooked egg noodles to the bowl with the sauce. Stir until everything is evenly coated.
Transfer the mixture to a greased 9×13-inch baking dish.
Sprinkle shredded cheddar cheese and shredded mozzarella cheese evenly over the top.
Bake in the preheated oven for 25 minutes, or until the casserole is bubbly and the cheese is melted and golden.
Remove from the oven and let it cool for 5 minutes before serving.