Preheat the oven to 390°F (200°C or 180°C fan).
Whisk the eggs, plain Greek yogurt, and 1/2 tsp kosher salt in a large bowl.
To a skillet over medium-high heat, add 2 tbsp of olive oil. When the oil is hot (after about 2 minutes), add the chopped broccolini. Sauté, stirring occasionally, until the broccolini is slightly charred and the stems are tender (about 8-10 minutes). Add 1/2 tsp kosher salt, the ground black pepper, and red pepper flakes.
Turn off the heat on the skillet and, if your skillet is ovenproof, add the whisked eggs, lightly stirring to distribute the broccolini evenly in the skillet. If the skillet is not ovenproof, transfer the broccolini to a baking dish (lightly brushed or sprayed with oil). Then, add the whisked eggs to the baking dish.
Reserve about a tablespoon of the shredded cheddar and shredded mozzarella. Add the rest of the cheddar and mozzarella to the frittata, and mix it in.
Top the frittata with the remaining cheddar, mozzarella, and all the parmesan.
Bake in the preheated oven at 390°F (200°C or 180°C fan) until golden and cooked through, for about 15 minutes. If using a baking dish (instead of an ovenproof skillet), it will take a couple of minutes longer (about 17-18 minutes) as the baking dish would have been cold when adding the ingredients so it would need a few minutes to get hot in the oven.
