Bring a medium pot of salted water to a boil and add the Brussels sprouts. Cook until crisp-tender, about 5 minutes. Drain.

In a large saucepan, melt 6 tablespoons of the butter over medium-high heat. Add the shallots and garlic, and cook for 1 minute. Add the sprouts in 1 layer and cook until golden brown, about 5 minutes. Remove from the pan. Add the remaining 2 tablespoons of butter and when melted, add the walnuts and cook, stirring, until golden and fragrant, about 2 minutes. Add the lemon juice, salt, pepper, and sprouts, and stir well to coat and warm through.

Transfer to a serving bowl and sprinkle with the Parmesan. Serve immediately.