This is a super great crowd-pleaser side for any holiday or dinner event, great served hot or at room temp or cold out of the fridge once everyone leaves. OJ is the surprise here! It mellows the lemon juice and you can grill people on what they think is the secret ingredient which is always a great way to get people to relax at a holiday meal...
Arrange an oven rack in the top third of the oven and preheat the broiler to high. Toss the broccolini with ¼ cup of the olive oil and the tablespoon of salt in a large bowl, then spread it out on a large rimmed sheet pan in a single layer (if doubling the recipe, use 2 sheet pans).
Put the lemon juice, orange juice, and a pinch of salt in a blender and blend on high. With the motor running, drizzle in the remaining ¼ cup olive oil until emulsified and lightened in color, 15 to 30 seconds. (You can also do all of this in a bowl if you don't want to bother with your blender.) There will be some extra dressing; if you double the recipe you'll have just enough, and if not store in an airtight container and use for up to 1 week).
Broil the broccolini until lightly charred, opening the oven and turning midway through, 2 to 3 minutes per side depending on your broiler (watch closely because it can burn very fast). Remove from the broiler and cool slightly, then add to the bowl with the dressing, add the shallots and 2 tablespoons of the parm, and toss to coat. Using tongs, transfer to a serving platter, sprinkle with the remaining 2 tablespoons of parm, and serve immediately.