- Position a rack in the lower third of an oven and preheat to 350°F. Coat the bottom of a roasting pan with 1 tablespoon of the oil.
- In a deep sauté pan over medium-high heat, warm 2 tablespoons of the olive oil. Add the carrots, celery and onion and sauté until tender and starting to caramelize, 8 to 10 minutes. Add the mushrooms and garlic and sauté for 1 minute. Let cool for 10 minutes.
- In a bowl, combine 1 1/2 cups of the bread crumbs and 1/3 cup of the mushroom soaking liquid and soak for 5 minutes. In another bowl, combine the remaining 3/4 cup bread crumbs, the 1 tablespoon parsley, the remaining 1 tablespoon olive oil, shredded cheese, salt and pepper.
- In a large bowl, using your hands, gently mix together the ground beef, soaked bread crumbs, vegetable mixture, eggs, the 1/4 cup parsley, thyme, cubed cheese, salt and pepper. Transfer the mixture to the prepared pan and shape into a 10-by-5-inch loaf. Cover the top and sides of the meat loaf with the cheese-bread crumb mixture.
- Bake until an instant-read thermometer inserted into the center of the meat loaf registers 165°F, about 1 hour and 10 minutes. Let the meat loaf rest for 5 minutes before slicing.
- Serve with mashed potatoes.