In a fine-mesh sieve, rinse the quinoa. Transfer to a large pot of boiling, salted water and cook until almost tender, about 12 minutes; drain in the sieve. In the same pot, bring enough water to reach a depth of 1 inch to a simmer over medium heat. Set the sieve with quinoa in the pot. Cover with a kitchen towel, then the lid, and steam until tender, about 10 minutes.
In a large skillet, heat 2 tablespoons olive oil over medium-high heat. Add the mushrooms and cook until lightly browned, 6 to 8 minutes. Stir in the scallion whites, pine nuts and dried currants; season with salt and pepper. Cook until the nuts are light golden, about 2 minutes; transfer to a bowl. In the same skillet, heat another 2 tablespoons olive oil over medium-high heat. Add the brussels sprouts and 1/8 cup water; season with salt and pepper. Cook until crisp-tender, about 8 minutes. Toss with the mushroom mixture, quinoa, scallion greens, parsley and remaining 2 tablespoons olive oil.