Heat a large pan over medium heat and then add the olive oil. Add the anchovy and use a wooden spoon to break it up in the oil. Add the chili flakes and garlic, stir to combine and cook until fragrant, about 1 minute.
Add the broccolini to the pan and stir to coat. Add 2-3 tablespoons of water to the pan and then cover to steam for 3 minutes. Uncover, stir, and then recover, cooking for 3 minutes longer. Uncover and turn up the heat to medium-high and cook until broccolini is charred in places.
Remove from heat and tansfer to a serving platter. Drizzle with lemon juice and top with shaved parmesan and fresh lemon zest. Serve topped with a fried egg or alongside grilled meat or chicken.