Preheat the oven to 400˚F.
Rinse the quinoa in a bowl of water, rubbing the seeds between the palms of your hands. Drain, and refill the bowl with fresh water. Repeat the rinse two more times.
Bring the water (or broth) to a simmer over medium-high heat in a medium pot. Slice the green onion into ½-inch pieces, and add to the simmering water, along with the quinoa. Return to a simmer, cover the pot, and reduce the heat to medium-low. Simmer until done, about 15 minutes. The liquid should be completely absorbed. Remove from heat and cool to room temperature.
Steam the broccoli in a medium pot until tender, about 5 minutes. Cool to room temperature.
Stir the remaining ingredients together in a large bowl until it looks like a smooth batter. Stir in the broccoli and one cup of the cooked quinoa, saving the rest for another use. Pour it all into the tart shell.
Bake on the middle rack for 30 minutes, or until set in the middle.