Preheat oven to 425 degrees. Add trimmed broccolini stalks to a large rimmed sheet pan and drizzle with olive oil. Season with salt and pepper. Bake for 15 minutes, or until fork tender. Remove and cool before roughly chopping.
In a small skillet, cook chopped bacon over medium-high heat until cooked and crispy. Remove from the pan with a slotted spoon and add in the chopped onion. Cook until translucent over medium heat, approximately 3 minutes. Remove from heat to cool.
Reduce oven temperature to 375 degrees. In the bowl of a food processor, or using your stand mixer with beater attachment, combine flour, salt, sugar and cold butter. Pulse (or beat) until the dough comes together.
Turn dough out onto a floured surface and roll out into a 12-inch circle. Add the dough to a pie dish pressing it up the sides and twisting the edges if desired (i.e. if you wanna get real fancy with it). Add pie weights to the center of the crust and bake for 20 minutes, until just starting to turn golden. Remove from oven to cool.
Keep oven on!
In a large bowl, whisk together the eggs until they are beaten well. Stir in cheese, onion, bacon and broccolini. Season lightly with salt and pepper before pouring into the cooked and cooled crust.
Bake quiche for 40 to 45 minutes, until the center is set. Serve immediately.