Heat a skillet over low heat and add the butter. Stir in the shallots and cook until caramelized, stirring often, about 25 minutes or so. Be sure to stir frequently since shallots are thinner than regular onions! Once caramely and golden, stir in the garlic and turn off the heat.
Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper and place the broccoli on the sheet, spread out. Drizzle with the olive oil and season with salt and pepper. Roast for 20 to 25 minutes, until just starting to char. When the broccolini is finished, reduce the oven heat to 350 degrees F. Chop the broccolini once it has cooled a bit.
While the broccolini is roasting, add the bacon to a large skillet over medium heat. Cook until the fat is rendered and the bacon is crispy, then remove the bacon with a slotted spoon. Place it on a paper towel to drain any excess grease. To the same skillet, add the potatoes. Cook until the potatoes are slightly crisp but tender when poked with a fork. Remove the potatoes and place them in a bowl.
Whisk together the eggs, cream, cheese, salt and pepper. Place half of the potatoes, bacon, brocc and shallots into the crust and pour the egg mixture over top. Add the remaining potatoes, bacon, broc and shallots, mixing them in gently. Bake for 55 to 60 minutes, or until golden on top and set in the center. Slice and serve with sriracha!