Preheat oven to 375 degrees. Lightly flour a rolling pin and work surface and roll out dough to a 12-inch round. Place in a 9-inch pie plate, fold overhang under, and crimp edge. Place a sheet of parchment paper over dough and fill with pie weights or dried beans. Bake until edge is dry and light golden, about 20 minutes. Remove parchment and weights.
Meanwhile, in a large skillet, melt butter over medium-high. Add onion, season with salt and pepper, and cook until light golden, 8 to 10 minutes. In a medium bowl, whisk together eggs and cream. Add onion, broccoli florets, and cheese and season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Whisk to combine, pour into crust, and bake until center of quiche is just set, 40 to 45 minutes. Serve warm or at room temperature.
To store, refrigerate cooled quiche, tightly covered, up to 3 days. To reheat quiche, cover with foil and place in a 325 degrees oven until warmed, about 15 minutes.
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