Cook the bacon in a large skillet over medium heat until crisp, 8 to 10 minutes. Using a slotted spoon, drain the bacon on paper towels.
For the rice: In a heavy saucepan or Dutch oven, bring the broth and thyme to a boil over medium-high heat. Add the brown and wild rice. Cover the saucepan and simmer until the rice is tender but still chewy, 30 minutes. Turn off the heat and allow the rice to stand for 10 minutes. Fluff with a fork.
For the vegetables: In the same skillet used to cook the bacon, heat the butter and oil over medium-high heat. Add the onions and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook, stirring occasionally until light golden, about 5 minutes. Add the mushrooms, 1/4 teaspoon salt and 1/4 teaspoon pepper. Cook until softened, about 8 minutes. Add the Brussels sprouts and the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Cook for 5 minutes.
Transfer the vegetable mixture to the saucepan of cooked rice. Add the hazelnuts and cooked bacon. Toss until all the ingredients are mixed. Transfer to a large bowl and serve.
The rice can also be cooked in 4 cups of broth and 1/2 cup of water. To toast the hazelnuts, arrange in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven until lightly toasted, 8 to 10 minutes. Cool completely before using.