Preheat the oven to 450 degrees F. Mince 1/2 red onion; cut the remaining 1 1/2 onions into 1/2-inch-thick wedges and set aside. Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Add the minced onion, mushrooms and 1 teaspoon thyme; season with salt and pepper. Cook, stirring, until the vegetables are tender, about 5 minutes.
Add the farro to the pot and cook, stirring, until toasted, about 1 minute. Add the wine and cook, stirring, until evaporated, 1 to 2 minutes. Add 5 cups water; bring to a boil. Reduce the heat to maintain a simmer and cook until the farro is tender and the liquid is mostly absorbed, 25 to 30 minutes.
Meanwhile, combine the onion wedges, butternut squash and the remaining 2 tablespoons olive oil and 1 teaspoon thyme in a large bowl; season with 1/2 teaspoon salt and a few grinds of pepper and toss. Spread on a rimmed baking sheet. Roast until the vegetables are tender and browned, about 25 minutes.
Add the cubed brie to the farro; stir until creamy. Stir in the parsley. Top each serving of farro with the vegetables and a slice of brie.