Rinse quinoa thoroughly in a fine mesh strainer for about two minutes to get rid of some of the bitterness. Drain well.
Meanwhile, toss broccoli with remaining 2 tablespoons olive oil, salt, and freshly ground black pepper. Roast for 15-20 minutes, until broccoli has browned a bit on the edges and is tender.
In a small saucepan, melt butter over low heat. Add pine nuts and cook for about 5-7 minutes, stirring occasionally, until butter is browned and pine nuts are toasted. Remove from heat, let cool slightly, and stir in red pepper flakes and lemon juice.
When quinoa is cooked, fluff slightly with a fork. Toss with broccoli, brown butter sauce and pine nuts, feta, and cilantro.