In 2 separate saucepans, cook the lentils and quinoa according to package directions. Let cool. Fluff the quinoa with a fork.
Meanwhile, halve the fennel bulbs lengthwise, then cut each half lengthwise into 3 wedges (you'll have 18 wedges total). Chop the fronds and measure out 6 tbsp. Divide the butter and 2 tbsp. EVOO between 2 large skillets; heat over medium heat. Divide the fennel in a single layer between the skillets and cook on one side until browned in spots, about 5 minutes. Flip the fennel and cook until browned on the other side, about 5 minutes. Divide the broth between the skillets. Cover and cook over low heat until the fennel is tender when pierced with a sharp knife, about 20 minutes; season with salt and pepper.
In a large bowl, toss the lentils with the fennel fronds, 1/4 cup EVOO, 1/4 cup parsley, the vinegar and mustard. Add the quinoa and toss gently; season with salt and pepper.
Transfer the pilaf to a large platter; top with the braised fennel. Drizzle with a little EVOO and sprinkle with more chopped parsley.